JEE Main & Advanced Mathematics Trigonometric Identities Question Bank

done Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles Total Questions - 93

• question_answer1)
  The angle subtended at the centre of a circle of radius 3 metres by an arc of length 1 metre is equal to [MNR 1973]
  A)
  \[{{20}^{o}}\] done clear
  B)
  \[{{60}^{o}}\] done clear
  C)
  \[\frac{1}{3}\] radian done clear
  D)
  3 radians done clear
  View Solution play_arrow

• question_answer2)
  A circular wire of radius \[7\,cm\] is cut and bend again into an arc of a circle of radius \[12cm\]. The angle subtended by the arc at the centre is [Kerala (Engg.) 2002]
  A)
  \[{{50}^{o}}\] done clear
  B)
  \[{{210}^{o}}\] done clear
  C)
  \[{{100}^{o}}\] done clear
  D)
  \[{{60}^{o}}\] done clear
  View Solution play_arrow

• question_answer3)
  The radius of the circle whose arc of length \[15cm\] makes an angle of 3/4 radian at the centre is [Karnataka CET 2002]
  A)
  \[10cm\] done clear
  B)
  \[20\,cm\] done clear
  C)
  \[11\frac{1}{4}cm\] done clear
  D)
  \[22\frac{1}{2}cm\] done clear
  View Solution play_arrow

• question_answer4)
  If for real values of \[x,\cos \theta =x+\frac{1}{x},\] then [MP PET 1996]
  A)
  \[\theta \] is an acute angle done clear
  B)
  \[\theta \] is a right angle done clear
  C)
  \[\theta \]is an obtuse angle done clear
  D)
  No value of \[\theta \]is possible done clear
  View Solution play_arrow

• question_answer5)
  The incorrect statement is [MNR 1993]
  A)
  \[\sin \theta =-\frac{1}{5}\] done clear
  B)
  \[\cos \theta =1\] done clear
  C)
  \[\sec \theta =\frac{1}{2}\] done clear
  D)
  \[\tan \theta =20\] done clear
  View Solution play_arrow

• question_answer6)
  Which of the following relations is possible
  A)
  \[\sin \theta =\frac{5}{3}\] done clear
  B)
  \[\tan \theta =1002\] done clear
  C)
  \[\cos \theta =\frac{1+{{p}^{2}}}{1-{{p}^{2}}},(p\ne \pm 1)\] done clear
  D)
  \[\sec \theta =\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer7)
  The equation \[{{(a+b)}^{2}}=4ab{{\sin }^{2}}\theta \]is possible only when
  A)
  \[2a=b\] done clear
  B)
  \[a=b\] done clear
  C)
  \[a=2b\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer8)
  The equation \[{{\sec }^{2}}\theta =\frac{4xy}{{{(x+y)}^{2}}}\]is only possible when [MP PET 1986; IIT 1996]
  A)
  \[x=y\] done clear
  B)
  \[x<y\] done clear
  C)
  \[x>y\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer9)
  Which of the following is correct
  A)
  \[\tan 1>\tan 2\] done clear
  B)
  \[\tan 1=\tan 2\] done clear
  C)
  \[\tan 1<\tan 2\] done clear
  D)
  \[\tan 1=1\] done clear
  View Solution play_arrow

• question_answer10)
  Which of the following relations is correct [WB JEE 1991]
  A)
  \[\sin 1<\sin 1{}^\circ \] done clear
  B)
  \[\sin 1>\sin 1{}^\circ \] done clear
  C)
  \[\sin 1=\sin 1{}^\circ \] done clear
  D)
  \[\frac{\pi }{180}\sin \,\,\,1\,=\sin \,\,\,{{1}^{o}}\] done clear
  View Solution play_arrow

• question_answer11)
  \[\tan 1{}^\circ \tan 2{}^\circ \tan 3{}^\circ \tan 4{}^\circ ........\tan 89{}^\circ =\]  [MP PET 1998, 2001; AMU 1999; Pb. CET 1994]
  A)
  1 done clear
  B)
  0 done clear
  C)
  \[\infty \] done clear
  D)
  1/2 done clear
  View Solution play_arrow

• question_answer12)
  If \[\sin \theta +\text{cosec}\theta =2,\] the value of \[{{\sin }^{10}}\theta +\text{cose}{{\text{c}}^{10}}\theta \] is [MP PET 2004]
  A)
  10 done clear
  B)
  \[{{2}^{10}}\] done clear
  C)
  \[{{2}^{9}}\] done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer13)
  If \[\sin \theta +\text{cosec}\theta =\text{2}\], then \[{{\sin }^{2}}\theta +\text{cose}{{\text{c}}^{\text{2}}}\theta =\] [MP PET 1992; MNR 1990; UPSEAT 2002]
  A)
  1 done clear
  B)
  4 done clear
  C)
  2 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer14)
  If \[\sin \theta +\cos \theta =m\]and \[\sec \theta +\text{cosec}\theta =n\], then \[n(m+1)(m-1)=\]       [MP PET 1986]
  A)
  m done clear
  B)
  n done clear
  C)
  2m done clear
  D)
  2n done clear
  View Solution play_arrow

• question_answer15)
  If \[\sin \theta +\cos \theta =1\], then \[\sin \theta \cos \theta =\] [Karnataka CET 1998]
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  1/2 done clear
  View Solution play_arrow

• question_answer16)
  If \[\sin \theta =\frac{24}{25}\]and \[\theta \] lies in the second quadrant, then \[\sec \theta +\tan \theta =\]        [MP PET 1997]
  A)
  - 3 done clear
  B)
  - 5 done clear
  C)
  - 7 done clear
  D)
  - 9 done clear
  View Solution play_arrow

• question_answer17)
  If \[\text{cosec }A+\cot A=\frac{11}{2},\] then \[\tan A=\] [Roorkee 1995]
  A)
  \[\frac{21}{22}\] done clear
  B)
  \[\frac{15}{16}\] done clear
  C)
  \[\frac{44}{117}\] done clear
  D)
  \[\frac{117}{43}\] done clear
  View Solution play_arrow

• question_answer18)
  If \[5\tan \theta =4,\] then \[\frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }=\] [Karnataka CET 1998]
  A)
  0 done clear
  B)
  1 done clear
  C)
  1/6 done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer19)
  .If \[\tan \theta =\frac{20}{21},\] cosq  will be [MP PET 1994]
  A)
  \[\pm \frac{20}{41}\] done clear
  B)
  \[\pm \frac{1}{21}\] done clear
  C)
  \[\pm \frac{21}{29}\] done clear
  D)
  \[\pm \frac{20}{21}\] done clear
  View Solution play_arrow

• question_answer20)
  If \[\sin x=\frac{-24}{25},\] then the value of \[\tan x\] is [UPSEAT 2003]
  A)
  \[\frac{24}{25}\] done clear
  B)
  \[\frac{-24}{7}\] done clear
  C)
  \[\frac{25}{24}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer21)
  If \[\tan \theta =\frac{-4}{3},\]then\[\sin \theta =\] [IIT 1979; Pb. CET 1995; Orissa JEE 2002]
  A)
  - 4/5 but not 4/5 done clear
  B)
  - 4/5 or 4/5 done clear
  C)
  4/5 but not - 4/5 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer22)
  If \[\sin \theta =-\frac{1}{\sqrt{2}}\] and \[\tan \theta =1,\] then \[\theta \] lies in which quadrant
  A)
  First done clear
  B)
  Second done clear
  C)
  Third done clear
  D)
  Fourth done clear
  View Solution play_arrow

• question_answer23)
  If \[\sin \theta =\frac{-4}{5}\] and \[\theta \] lies in the third quadrant, then \[\cos \frac{\theta }{2}=\]
  A)
  \[\frac{1}{\sqrt{5}}\] done clear
  B)
  \[-\frac{1}{\sqrt{5}}\] done clear
  C)
  \[\sqrt{\frac{2}{5}}\] done clear
  D)
  \[-\sqrt{\frac{2}{5}}\] done clear
  View Solution play_arrow

• question_answer24)
  If \[\sin (\alpha -\beta )=\frac{1}{2}\]and \[\cos (\alpha +\beta )=\frac{1}{2},\]where \[\alpha \] and \[\beta \] are positive acute angles, then
  A)
  \[\alpha =45{}^\circ ,\beta =15{}^\circ \] done clear
  B)
  \[\alpha =15{}^\circ ,\beta =45{}^\circ \] done clear
  C)
  \[\alpha =60{}^\circ ,\beta =15{}^\circ \] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer25)
  If \[\tan \theta =-\frac{1}{\sqrt{10}}\]and \[\theta \] lies in the fourth quadrant, then \[\cos \theta =\]
  A)
  \[1/\sqrt{11}\] done clear
  B)
  \[-1/\sqrt{11}\] done clear
  C)
  \[\sqrt{\frac{10}{11}}\] done clear
  D)
  \[-\sqrt{\frac{10}{11}}\] done clear
  View Solution play_arrow

• question_answer26)
  \[(m+2)\sin \theta +(2m-1)\cos \theta =2m+1,\]if
  A)
  \[\tan \theta =\frac{3}{4}\] done clear
  B)
  \[\tan \theta =\frac{4}{3}\] done clear
  C)
  \[\tan \theta =\frac{2m}{{{m}^{2}}+1}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer27)
  If \[A\] lies in the second quadrant and \[3\tan A+4=0,\] the value of \[2\cot A-5\cos A+\sin A\]is equal to [Pb. CET 2000]
  A)
  \[\frac{-53}{10}\] done clear
  B)
  \[\frac{-7}{10}\] done clear
  C)
  \[\frac{7}{10}\] done clear
  D)
  \[\frac{23}{10}\] done clear
  View Solution play_arrow

• question_answer28)
  If \[\sin x+\sin y=3(\cos y-\cos x),\] then the value of \[\frac{\sin 3x}{\sin 3y}\] is
  A)
  1 done clear
  B)
  - 1 done clear
  C)
  0 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer29)
  If \[\sin A,\cos A\] and \[\tan A\] are in G.P., then \[{{\cos }^{3}}A+{{\cos }^{2}}A\] is equal to
  A)
  1 done clear
  B)
  2 done clear
  C)
  4 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer30)
  If \[\theta \] lies in the second quadrant, then the value of \[\sqrt{\left( \frac{1-\sin \theta }{1+\sin \theta } \right)}+\sqrt{\left( \frac{1+\sin \theta }{1-\sin \theta } \right)}\]
  A)
  \[2\sec \theta \] done clear
  B)
  \[-2\sec \theta \] done clear
  C)
  \[2\text{cosec}\theta \] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer31)
  \[\frac{\sin \theta }{1-\cot \theta }+\frac{\cos \theta }{1-\tan \theta }=\]     [Karnataka CET 1998]
  A)
  0 done clear
  B)
  1 done clear
  C)
  \[\cos \theta -\sin \theta \] done clear
  D)
  \[\cos \theta +\sin \theta \] done clear
  View Solution play_arrow

• question_answer32)
  If \[\tan \theta +\sec \theta ={{e}^{x}},\]then \[\cos \theta \] equals [AMU 2002]
  A)
  \[\frac{({{e}^{x}}+{{e}^{-x}})}{2}\] done clear
  B)
  \[\frac{2}{({{e}^{x}}+{{e}^{-x}})}\] done clear
  C)
  \[\frac{({{e}^{x}}-{{e}^{-x}})}{2}\] done clear
  D)
  \[\frac{({{e}^{x}}-{{e}^{-x}})}{({{e}^{x}}+{{e}^{-x}})}\] done clear
  View Solution play_arrow

• question_answer33)
  If \[\cos \theta -\sin \theta =\sqrt{2}\sin \theta ,\]then \[\cos \theta +\sin \theta \]is equal to  [WB JEE 1988]
  A)
  \[\sqrt{2}\cos \theta \] done clear
  B)
  \[\sqrt{2}\sin \theta \] done clear
  C)
  \[2\cos \theta \] done clear
  D)
  \[-\sqrt{2}\cos \theta \] done clear
  View Solution play_arrow

• question_answer34)
  If \[\sec \theta +\tan \theta =p,\]then \[\tan \theta \]is equal to [MP PET 1994]
  A)
  \[\frac{2p}{{{p}^{2}}-1}\] done clear
  B)
  \[\frac{{{p}^{2}}-1}{2p}\] done clear
  C)
  \[\frac{{{p}^{2}}+1}{2p}\] done clear
  D)
  \[\frac{2p}{{{p}^{2}}+1}\] done clear
  View Solution play_arrow

• question_answer35)
  If \[x=\sec \theta +\tan \theta ,\]then \[x+\frac{1}{x}=\] [MP PET 1986]
  A)
  1 done clear
  B)
  \[2\sec \theta \] done clear
  C)
  2 done clear
  D)
  \[2\tan \theta \] done clear
  View Solution play_arrow

• question_answer36)
  If \[x+\frac{1}{x}=2\cos \alpha \], then \[{{x}^{n}}+\frac{1}{{{x}^{n}}}=\] [Karnataka CET 2004]
  A)
  \[{{2}^{n}}\cos \alpha \] done clear
  B)
  \[{{2}^{n}}\cos n\alpha \] done clear
  C)
  \[2i\,\sin \,n\,\alpha \] done clear
  D)
  \[2\cos \,n\alpha \] done clear
  View Solution play_arrow

• question_answer37)
  If \[\cos \theta =\frac{1}{2}\left( x+\frac{1}{x} \right)\], then \[\frac{1}{2}\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)=\] [AMU 1998]
  A)
  \[\sin 2\theta \] done clear
  B)
  \[\cos \,2\theta \] done clear
  C)
  \[\tan \,2\theta \] done clear
  D)
  \[\sec \,2\theta \] done clear
  View Solution play_arrow

• question_answer38)
  The value of \[{{e}^{{{\log }_{10}}\tan 1{}^\circ +{{\log }_{10}}\tan 2{}^\circ +{{\log }_{10}}\tan 3{}^\circ +...........+{{\log }_{10}}\tan 89{}^\circ }}\] is
  A)
  0 done clear
  B)
  e done clear
  C)
  1/e done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer39)
  \[\cot x-\tan x=\]       [MP PET 1986]
  A)
  \[\cot \,2x\] done clear
  B)
  \[2{{\cot }^{2}}x\] done clear
  C)
  \[2\,\,\cot \,2x\] done clear
  D)
  \[{{\cot }^{2}}\,2x\] done clear
  View Solution play_arrow

• question_answer40)
  \[\frac{1+\sin A-\cos A}{1+\sin A+\cos A}\]= 
  A)
  \[\sin \frac{A}{2}\] done clear
  B)
  \[\cos \frac{A}{2}\] done clear
  C)
  \[\tan \frac{A}{2}\] done clear
  D)
  \[\cot \frac{A}{2}\] done clear
  View Solution play_arrow

• question_answer41)
  \[\frac{2\sin \theta \,\tan \theta (1-\tan \theta )+2\sin \theta {{\sec }^{2}}\theta }{{{(1+\tan \theta )}^{2}}}=\] [Roorkee 1975]
  A)
  \[\frac{\sin \,\theta }{1+\tan \theta }\] done clear
  B)
  \[\frac{2\,\sin \theta }{1+\tan \theta }\] done clear
  C)
  \[\frac{2\sin \theta }{{{(1+\tan \theta )}^{2}}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer42)
  The value of the expression\[1-\frac{{{\sin }^{2}}y}{1+\cos \,y}+\frac{1+\cos \,y}{\sin \,y}-\frac{\sin \,\,y}{1-\cos \,y}\]is equal to
  A)
  0 done clear
  B)
  1 done clear
  C)
  \[\sin \,y\] done clear
  D)
  \[\cos \,y\] done clear
  View Solution play_arrow

• question_answer43)
  If \[2y\,\cos \theta =x\sin \,\theta \text{ and }2x\sec \theta -y\,\text{cosec}\,\theta =3,\] then \[{{x}^{2}}+4{{y}^{2}}=\]   [WB JEE 1988]
  A)
  4 done clear
  B)
  - 4 done clear
  C)
  ± 4 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer44)
  If \[\tan A+\cot A=4,\]then \[{{\tan }^{4}}A+{{\cot }^{4}}A\] is equal to   [Kerala (Engg.) 2002]
  A)
  110 done clear
  B)
  191 done clear
  C)
  80 done clear
  D)
  194 done clear
  View Solution play_arrow

• question_answer45)
  If \[x=\sec \,\varphi -\tan \varphi ,y=\text{cosec}\varphi +\cot \varphi ,\]then
  A)
  \[x=\frac{y+1}{y-1}\] done clear
  B)
  \[x=\frac{y-1}{y+1}\] done clear
  C)
  \[y=\frac{1-x}{1+x}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer46)
  If \[\tan \theta =\frac{x\,\sin \,\varphi }{1-x\,\cos \,\varphi }\] and \[\tan \,\varphi =\frac{y\sin \,\theta }{1-y\,\cos \,\theta }\], then \[\frac{x}{y}=\] [MP PET 1991]
  A)
  \[\frac{\sin \varphi }{\sin \theta }\] done clear
  B)
  \[\frac{\sin \theta }{\sin \varphi }\] done clear
  C)
  \[\frac{\sin \varphi }{1-\cos \theta }\] done clear
  D)
  \[\frac{\sin \theta }{1-\cos \varphi }\] done clear
  View Solution play_arrow

• question_answer47)
  If \[p=\frac{2\sin \,\theta }{1+\cos \theta +\sin \theta }\], and \[q=\frac{\cos \theta }{1+\sin \theta },\] then [MP PET 2001]
  A)
  \[pq=1\] done clear
  B)
  \[\frac{q}{p}=1\] done clear
  C)
  \[q-p=1\] done clear
  D)
  \[q+p=1\] done clear
  View Solution play_arrow

• question_answer48)
  If \[\tan \theta +\sin \theta =m\]and \[\tan \theta -\sin \theta =n,\]then [IIT 1970]
  A)
  \[{{m}^{2}}-{{n}^{2}}=4mn\] done clear
  B)
  \[{{m}^{2}}+{{n}^{2}}=4mn\] done clear
  C)
  \[{{m}^{2}}-{{n}^{2}}={{m}^{2}}+{{n}^{2}}\] done clear
  D)
  \[{{m}^{2}}-{{n}^{2}}=4\sqrt{mn}\] done clear
  View Solution play_arrow

• question_answer49)
  If \[\tan \theta =\frac{a}{b},\]then \[\frac{\sin \theta }{{{\cos }^{8}}\theta }+\frac{\cos \theta }{{{\sin }^{8}}\theta }=\] [WB JEE 1986]
  A)
  \[\pm \frac{{{({{a}^{2}}+{{b}^{2}})}^{4}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\left( \frac{a}{{{b}^{8}}}+\frac{b}{{{a}^{8}}} \right)\] done clear
  B)
  \[\pm \frac{{{({{a}^{2}}+{{b}^{2}})}^{4}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\left( \frac{a}{{{b}^{8}}}-\frac{b}{{{a}^{8}}} \right)\] done clear
  C)
  \[\pm \frac{{{({{a}^{2}}-{{b}^{2}})}^{4}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\left( \frac{a}{{{b}^{8}}}+\frac{b}{{{a}^{8}}} \right)\] done clear
  D)
  \[\pm \frac{{{({{a}^{2}}-{{b}^{2}})}^{4}}}{\sqrt{{{a}^{2}}-{{b}^{2}}}}\left( \frac{a}{{{b}^{8}}}-\frac{b}{{{a}^{8}}} \right)\] done clear
  View Solution play_arrow

• question_answer50)
  If \[a\cos \theta +b\sin \theta =m\] and \[a\sin \theta -b\cos \theta =n,\] then \[{{a}^{2}}+{{b}^{2}}=\]
  A)
  \[m+n\] done clear
  B)
  \[{{m}^{2}}-{{n}^{2}}\] done clear
  C)
  \[{{m}^{2}}+{{n}^{2}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer51)
  If \[x=a{{\cos }^{3}}\theta ,y=b{{\sin }^{3}}\theta ,\]then
  A)
  \[{{\left( \frac{a}{x} \right)}^{2/3}}+{{\left( \frac{b}{y} \right)}^{2/3}}=1\] done clear
  B)
  \[{{\left( \frac{b}{x} \right)}^{2/3}}+{{\left( \frac{a}{y} \right)}^{2/3}}=1\] done clear
  C)
  \[{{\left( \frac{x}{a} \right)}^{2/3}}+{{\left( \frac{y}{b} \right)}^{2/3}}=1\] done clear
  D)
  \[{{\left( \frac{x}{b} \right)}^{2/3}}+{{\left( \frac{y}{a} \right)}^{2/3}}=1\] done clear
  View Solution play_arrow

• question_answer52)
  If \[\cot \,\theta +\tan \theta =m\]and \[\sec \theta -\cos \theta =n,\]then which of the following is correct
  A)
  \[m{{(m{{n}^{2}})}^{1/3}}-n{{(n{{m}^{2}})}^{1/3}}=1\] done clear
  B)
  \[m{{({{m}^{2}}n)}^{1/3}}-n{{(m{{n}^{2}})}^{1/3}}=1\] done clear
  C)
  \[n{{(m{{n}^{2}})}^{1/3}}-m{{(n{{m}^{2}})}^{1/3}}=1\] done clear
  D)
  \[n{{({{m}^{2}}n)}^{1/3}}-m{{(m{{n}^{2}})}^{1/3}}=1\] done clear
  View Solution play_arrow

• question_answer53)
  \[{{\sin }^{6}}\theta +{{\cos }^{6}}\theta +3{{\sin }^{2}}\theta {{\cos }^{2}}\theta =\] [MP PET 1995, 2002; DCE 2005]
  A)
  0 done clear
  B)
  -1 done clear
  C)
  1 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer54)
  The value of \[2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1\] is  [MP PET 1997; UPSEAT 2002]
  A)
  2 done clear
  B)
  0 done clear
  C)
  4 done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer55)
  If \[\sin x+{{\sin }^{2}}x=1\], then the value of \[{{\cos }^{12}}x+3{{\cos }^{10}}x+3{{\cos }^{8}}x+{{\cos }^{6}}x-2\] is equal to  [Pb. CET 2002]
  A)
  0 done clear
  B)
  1 done clear
  C)
  - 1 done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer56)
  If \[\cos x+{{\cos }^{2}}x=1,\]then the value of \[{{\sin }^{2}}x+{{\sin }^{4}}x\] is
  A)
  1 done clear
  B)
  -1 done clear
  C)
  0 done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer57)
  If \[\sin x+{{\sin }^{2}}x=1,\]then \[{{\cos }^{8}}x+2{{\cos }^{6}}x+{{\cos }^{4}}x=\]
  A)
  0 done clear
  B)
  -1 done clear
  C)
  2 done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer58)
  If \[x{{\sin }^{3}}\alpha +y{{\cos }^{3}}\alpha =\sin \alpha \cos \alpha \] and \[x\sin \alpha -y\cos \alpha =0,\] then \[{{x}^{2}}+{{y}^{2}}=\] [WB JEE 1984]
  A)
  - 1 done clear
  B)
  ±1 done clear
  C)
  1 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer59)
  If \[(1+\sin A)(1+\sin B)(1+\sin C)\]\[=(1-\sin A)(1-\sin B)(1-\sin C),\]then each side is equal to
  A)
  \[\pm \sin A\sin B\sin C\] done clear
  B)
  \[\pm \cos A\cos B\cos C\] done clear
  C)
  \[\pm \sin A\cos B\cos C\] done clear
  D)
  \[\pm \cos A\sin B\sin C\] done clear
  View Solution play_arrow

• question_answer60)
  If \[(\sec \alpha +\tan \alpha )(\sec \beta +\tan \beta )(\sec \gamma +\tan \gamma )\]\[=\tan \alpha \tan \beta \tan \gamma \], then \[(\sec \alpha -\tan \alpha )(\sec \beta -\tan \beta )\] \[(\sec \gamma -\tan \gamma )=\]        [Kurukshetra CEE 1998]
  A)
  \[\cot \alpha \cot \beta \cot \gamma \] done clear
  B)
  \[\tan \alpha \tan \beta \tan \gamma \] done clear
  C)
  \[\cot \alpha +\cot \beta +\cot \gamma \] done clear
  D)
  \[\tan \alpha +\tan \beta +\tan \gamma \] done clear
  View Solution play_arrow

• question_answer61)
  If \[\sin {{\theta }_{1}}+\sin {{\theta }_{2}}+\sin {{\theta }_{3}}=3,\]then \[\cos {{\theta }_{1}}+\cos {{\theta }_{2}}+\cos {{\theta }_{3}}=\]   [EAMCET 1994]
  A)
  3 done clear
  B)
  2 done clear
  C)
  1 done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer62)
  If \[{{\sin }^{2}}\theta =\frac{{{x}^{2}}+{{y}^{2}}+1}{2x}\], then x must be  [UPSEAT 2004]
  A)
  - 3 done clear
  B)
  - 2 done clear
  C)
  1 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer63)
  If \[\tan \theta -\cot \theta =a\] and \[\sin \theta +\cos \theta =b,\] then \[{{({{b}^{2}}-1)}^{2}}({{a}^{2}}+4)\] is equal to [WB JEE 1979]
  A)
  2 done clear
  B)
  - 4 done clear
  C)
  ± 4 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer64)
  If \[{{\tan }^{2}}\alpha {{\tan }^{2}}\beta +{{\tan }^{2}}\beta {{\tan }^{2}}\gamma +{{\tan }^{2}}\gamma {{\tan }^{2}}\alpha \]\[+2{{\tan }^{2}}\alpha {{\tan }^{2}}\beta {{\tan }^{2}}\gamma =1,\]then the value of\[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma \]is  
  A)
  0 done clear
  B)
  -1 done clear
  C)
  1 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer65)
  \[\cos 1{}^\circ .\cos 2{}^\circ .\cos 3{}^\circ .........\cos 179{}^\circ =\] [Karnataka CET 1999; DCE 2005]
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer66)
  The value of \[\frac{\cot 54{}^\circ }{\tan 36{}^\circ }+\frac{\tan 20{}^\circ }{\cot 70{}^\circ }\] is [Karnataka CET 1999]
  A)
  2 done clear
  B)
  3 done clear
  C)
  1 done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer67)
  The value of \[\sin 10{}^\circ +\sin 20{}^\circ +\sin 30{}^\circ +...+\] \[\sin 360{}^\circ \] is  [Pb. CET 2003]
  A)
  1 done clear
  B)
  0 done clear
  C)
  - 1 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer68)
  \[\cos 1{}^\circ +\cos 2{}^\circ +\cos 3{}^\circ +.....+\cos 180{}^\circ =\] [Karnataka CET 2003]
  A)
  0 done clear
  B)
  1 done clear
  C)
  -1 done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer69)
  If \[\alpha =22{}^\circ 30',\]then \[(1+\cos \alpha )(1+\cos 3\alpha )\] \[(1+\cos 5\alpha )(1+\cos 7\alpha )\] equals        [AMU 1999]
  A)
  1/8 done clear
  B)
  1/4 done clear
  C)
  \[\frac{1+\sqrt{2}}{2\sqrt{2}}\] done clear
  D)
  \[\frac{\sqrt{2}-1}{\sqrt{2}+1}\] done clear
  View Solution play_arrow

• question_answer70)
  The value of  \[6({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-9({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+4\] is [MP PET 2001]
  A)
  -3 done clear
  B)
  0 done clear
  C)
  1 done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer71)
  \[\sin 15{}^\circ +\cos 105{}^\circ =\]        [MP PET 1992]
  A)
  0 done clear
  B)
  \[2\sin 15{}^\circ \] done clear
  C)
  \[\cos 15{}^\circ +\sin 15{}^\circ \] done clear
  D)
  \[\sin 15{}^\circ -\cos 15{}^\circ \] done clear
  View Solution play_arrow

• question_answer72)
  The value \[\cos 105{}^\circ +\sin 105{}^\circ \]is [MNR 1975]
  A)
  \[\frac{1}{2}\] done clear
  B)
  1 done clear
  C)
  \[\sqrt{2}\] done clear
  D)
  \[\frac{1}{\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer73)
  The value of \[\cos y\cos \left( \frac{\pi }{2}-x \right)-\cos \left( \frac{\pi }{2}-y \right)\cos x\] \[+\sin y\cos \left( \frac{\pi }{2}-x \right)+\cos x\sin \left( \frac{\pi }{2}-y \right)\] is zero, if
  A)
  \[x=0\] done clear
  B)
  \[y=0\] done clear
  C)
  \[x=y\] done clear
  D)
  \[x=n\pi -\frac{\pi }{4}+y,\,\,(n\in I)\] done clear
  View Solution play_arrow

• question_answer74)
  \[\sin \left( \frac{\pi }{10} \right)\sin \left( \frac{3\pi }{10} \right)=\]        [MNR 1984]
  A)
  1/2 done clear
  B)
  -1/2 done clear
  C)
  1/4 done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer75)
  If \[x\sin 45{}^\circ {{\cos }^{2}}60{}^\circ =\frac{{{\tan }^{2}}60{}^\circ \text{cosec}30{}^\circ }{\sec 45{}^\circ {{\cot }^{2}}30{}^\circ },\] then \[x=\]
  A)
  2 done clear
  B)
  4 done clear
  C)
  8 done clear
  D)
  16 done clear
  View Solution play_arrow

• question_answer76)
  If \[A=130{}^\circ \]and \[x=\sin A+\cos A,\]then [CET 1989]
  A)
  \[x>0\] done clear
  B)
  \[x<0\] done clear
  C)
  \[x=0\] done clear
  D)
  \[x\le 0\] done clear
  View Solution play_arrow

• question_answer77)
  \[\cos A+\sin (270{}^\circ +A)-\sin (270{}^\circ -A)+\cos (180{}^\circ +A)=\] [MP PET 1990]
  A)
  -1 done clear
  B)
  0 done clear
  C)
  1 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer78)
  If \[\pi <\alpha <\frac{3\pi }{2}\], then \[\sqrt{\frac{1-\cos \alpha }{1+\cos \alpha }}+\sqrt{\frac{1+\cos \alpha }{1-\cos \alpha }}\]=
  A)
  \[\frac{2}{\sin \alpha }\] done clear
  B)
  \[-\frac{2}{\sin \alpha }\] done clear
  C)
  \[\frac{1}{\sin \alpha }\] done clear
  D)
  \[-\frac{1}{\sin \alpha }\] done clear
  View Solution play_arrow

• question_answer79)
  \[\tan \left( \frac{\pi }{4}+\theta  \right)-\tan \left( \frac{\pi }{4}-\theta  \right)=\]
  A)
  \[2\tan 2\theta \] done clear
  B)
  \[2\cot 2\theta \] done clear
  C)
  \[\tan 2\theta \] done clear
  D)
  \[\cot 2\theta \] done clear
  View Solution play_arrow

• question_answer80)
  \[\sin (\pi +\theta )\sin (\pi -\theta )\,\text{ cose}{{\text{c}}^{2}}\theta =\] [EAMCET 1980]
  A)
  1 done clear
  B)
  \[1\] done clear
  C)
  \[\sin \theta \] done clear
  D)
  \[-\sin \theta \] done clear
  View Solution play_arrow

• question_answer81)
  \[\cot (45{}^\circ +\theta )\cot (45{}^\circ -\theta )=\] [MNR 1973]
  A)
  -1 done clear
  B)
  0 done clear
  C)
  1 done clear
  D)
  done clear
  View Solution play_arrow

• question_answer82)
  \[\tan A+\cot (180{}^\circ +A)+\cot (90{}^\circ +A)+\cot (360{}^\circ -A)\]     [MP PET 1992]
  A)
  0 done clear
  B)
  \[2\tan A\] done clear
  C)
  \[2\cot A\] done clear
  D)
  \[2(\tan A-\cot A)\] done clear
  View Solution play_arrow

• question_answer83)
  \[\tan \theta \sin \left( \frac{\pi }{2}+\theta  \right)\cos \left( \frac{\pi }{2}-\theta  \right)=\] [EAMCET 1981]
  A)
  1 done clear
  B)
  0 done clear
  C)
  \[\frac{1}{\sqrt{2}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer84)
  If angle \[\theta \] be divided into two parts such that the tangent of one part is \[k\] times the tangent of the other and \[\varphi \] is their difference, then \[\sin \theta =\]
  A)
  \[\frac{k+1}{k-1}\sin \varphi \] done clear
  B)
  \[\frac{k-1}{k+1}\sin \varphi \] done clear
  C)
  \[\frac{2k-1}{2k+1}\sin \varphi \] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer85)
  If \[x=y\cos \frac{2\pi }{3}=z\cos \frac{4\pi }{3}\], then \[xy+yz+zx=\] [EAMCET 1994]
  A)
  -1 done clear
  B)
  0 done clear
  C)
  1 done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer86)
  Given that \[\pi <\alpha <\frac{3\pi }{2},\] then the expression \[\sqrt{(4{{\sin }^{4}}\alpha +{{\sin }^{2}}2\alpha )}+4{{\cos }^{2}}\left( \frac{\pi }{4}-\frac{\alpha }{2} \right)\] is equal to   
  A)
  2 done clear
  B)
  \[2+4\sin \alpha \] done clear
  C)
  \[2-4\sin \alpha \] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer87)
  \[{{\sin }^{2}}\frac{\pi }{8}+{{\sin }^{2}}\frac{3\pi }{8}+{{\sin }^{2}}\frac{5\pi }{8}+{{\sin }^{2}}\frac{7\pi }{8}=\]
  A)
  1 done clear
  B)
  -1 done clear
  C)
  0 done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer88)
  \[(\sec A+\tan A-1)(\sec A-\tan A+1)-2\tan A=\][Roorkee 1972]
  A)
  \[\sec A\] done clear
  B)
  \[2\sec A\] done clear
  C)
  0 done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer89)
  The value of \[\tan (-945{}^\circ )\] is [MP PET 1997]
  A)
  - 1 done clear
  B)
  - 2 done clear
  C)
  - 3 done clear
  D)
  - 4 done clear
  View Solution play_arrow

• question_answer90)
  If \[\tan A=\frac{1}{2},\tan B=\frac{1}{3},\]then \[\cos 2A=\] [CET 1989]
  A)
  \[\sin B\] done clear
  B)
  \[\sin 2B\] done clear
  C)
  \[\sin 3B\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer91)
  The value of \[\cos A-\sin A\]when \[A=\frac{5\pi }{4},\]is [MP PET 1990]
  A)
  \[\sqrt{2}\] done clear
  B)
  \[\frac{1}{\sqrt{2}}\] done clear
  C)
  0 done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer92)
  The value of \[\cos (270{}^\circ +\theta )\,\cos (90{}^\circ -\theta )-\sin (270{}^\circ -\theta )\,\cos \theta \] is [Karnataka CET 2005]
  A)
  0 done clear
  B)
  -1 done clear
  C)
  1/2 done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer93)
  If \[\cos (\alpha -\beta )=1\] and \[\cos (\alpha +\beta )=\frac{1}{e}\], \[-\pi <\alpha ,\beta <\pi \], then total number of ordered pair of \[(\alpha ,\beta )\] is [IIT Screening 2005]
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  4 done clear
  View Solution play_arrow