JEE Main & Advanced Mathematics Trigonometric Identities Question Bank

done Trigonometrical ratios of sum and difference of two and three angles Total Questions - 85

• question_answer1)
  If \[\sin A=\frac{1}{\sqrt{10}}\]and \[\sin B=\frac{1}{\sqrt{5}},\]where A and B are positive acute angles, then \[A+B=\] [MP PET 1986]
  A)
  \[\pi \] done clear
  B)
  \[\pi /2\] done clear
  C)
  \[\pi /3\] done clear
  D)
  \[\pi /4\] done clear
  View Solution play_arrow

• question_answer2)
  If \[\tan A=2\tan B+\cot B,\]then \[2\tan (A-B)=\]
  A)
  \[\tan B\] done clear
  B)
  \[2\tan B\] done clear
  C)
  \[\cot B\] done clear
  D)
  \[2\cot B\] done clear
  View Solution play_arrow

• question_answer3)
  If \[\sin A+\sin B=C,\cos A+\cos B=D,\]then the value of \[\sin (A+B)=\]        [MP PET 1986]
  A)
  \[CD\] done clear
  B)
  \[\frac{CD}{{{C}^{2}}+{{D}^{2}}}\] done clear
  C)
  \[\frac{{{C}^{2}}+{{D}^{2}}}{2\,CD}\] done clear
  D)
  \[\frac{2\,CD}{{{C}^{2}}+{{D}^{2}}}\] done clear
  View Solution play_arrow

• question_answer4)
  If \[\sin A=\sin B\]and \[\cos A=\cos B,\]then [EAMCET 1994]
  A)
  \[\sin \frac{A-B}{2}=0\] done clear
  B)
  \[\sin \frac{A+B}{2}=0\] done clear
  C)
  \[\cos \frac{A-B}{2}=0\] done clear
  D)
  \[\cos (A+B)=0\] done clear
  View Solution play_arrow

• question_answer5)
  \[\sin 50{}^\circ -\sin 70{}^\circ +\sin 10{}^\circ =\] [MNR 1979]
  A)
  1 done clear
  B)
  0 done clear
  C)
  1/2 done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer6)
  \[{{\cos }^{2}}48{}^\circ -{{\sin }^{2}}12{}^\circ =\]      [MNR 1977]
  A)
  \[\frac{\sqrt{5}-1}{4}\] done clear
  B)
  \[\frac{\sqrt{5}+1}{8}\] done clear
  C)
  \[\frac{\sqrt{3}-1}{4}\] done clear
  D)
  \[\frac{\sqrt{3}+1}{2\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer7)
  If \[y=(1+\tan A)(1-\tan B)\] where \[A-B=\frac{\pi }{4}\], then \[{{(y+1)}^{y+1}}\] is equal to [J & K 2005]
  A)
  9 done clear
  B)
  4 done clear
  C)
  27 done clear
  D)
  81 done clear
  View Solution play_arrow

• question_answer8)
  \[\sin 75{}^\circ =\]        [MNR 1979]
  A)
  \[\frac{2-\sqrt{3}}{2}\] done clear
  B)
  \[\frac{\sqrt{3}+1}{2\sqrt{2}}\] done clear
  C)
  \[\frac{\sqrt{3}-1}{-2\sqrt{2}}\] done clear
  D)
  \[\frac{\sqrt{3}-1}{2\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer9)
  If \[\tan \alpha =\frac{m}{m+1}\]and \[\tan \beta =\frac{1}{2m+1}\], then \[\alpha +\beta =\] [IIT 1978; EAMCET 1992; Roorkee 1998; JMI EEE 2001]
  A)
  \[\frac{\pi }{3}\] done clear
  B)
  \[\frac{\pi }{4}\] done clear
  C)
  \[\frac{\pi }{6}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer10)
  \[\tan 20{}^\circ +\tan 40{}^\circ +\sqrt{3}\tan 20{}^\circ \tan 40{}^\circ =\]
  A)
  \[\frac{1}{\sqrt{3}}\] done clear
  B)
  \[\sqrt{3}\] done clear
  C)
  \[-\frac{1}{\sqrt{3}}\] done clear
  D)
  \[-\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer11)
  \[\frac{1}{4}\left[ \sqrt{3}\cos 23{}^\circ -\sin 23{}^\circ  \right]=\]
  A)
  \[\cos 43{}^\circ \] done clear
  B)
  \[\cos 7{}^\circ \] done clear
  C)
  \[\cos 53{}^\circ \] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  \[\tan 75{}^\circ -\cot 75{}^\circ =\] [MNR 1982; Pb. CET 1990, 2000]
  A)
  \[2\sqrt{3}\] done clear
  B)
  \[2+\sqrt{3}\] done clear
  C)
  \[2-\sqrt{3}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer13)
  If \[\tan A=-\frac{1}{2}\]and \[\tan B=-\frac{1}{3},\]then \[A+B=\] [IIT 1967; MNR 1987; MP PET 1989]
  A)
  \[\frac{\pi }{4}\] done clear
  B)
  \[\frac{3\pi }{4}\] done clear
  C)
  \[\frac{5\pi }{4}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer14)
  If \[A+B=225{}^\circ ,\]then\[\frac{\cot A}{1+\cot A}.\frac{\cot B}{1+\cot B}=\] [MNR 1974]
  A)
  1 done clear
  B)
  - 1 done clear
  C)
  0 done clear
  D)
  1/2 done clear
  View Solution play_arrow

• question_answer15)
  If \[\sin A=\frac{4}{5}\]and \[\cos B=-\frac{12}{13},\]where A and B lie in first and third quadrant respectively, then \[\cos (A+B)=\]
  A)
  \[\frac{56}{65}\] done clear
  B)
  \[-\frac{56}{65}\] done clear
  C)
  \[\frac{16}{65}\] done clear
  D)
  \[-\frac{16}{65}\] done clear
  View Solution play_arrow

• question_answer16)
  If \[A+B=\frac{\pi }{4},\]then \[(1+\tan A)(1+\tan B)=\]
  A)
  1 done clear
  B)
  2 done clear
  C)
  \[\infty \] done clear
  D)
  -2 done clear
  View Solution play_arrow

• question_answer17)
  \[\frac{1}{\sin 10{}^\circ }-\frac{\sqrt{3}}{\cos 10{}^\circ }\]=     [IIT 1974]
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer18)
  If \[\cos (A+B)=\alpha \cos A\cos B+\beta \sin A\sin B,\]then \[(\alpha ,\beta )\]=  [MP PET 1992]
  A)
  (-1, -1) done clear
  B)
  (- 1, 1) done clear
  C)
  (1, -1) done clear
  D)
  (1, 1) done clear
  View Solution play_arrow

• question_answer19)
  \[\frac{{{\sin }^{2}}A-{{\sin }^{2}}B}{\sin A\cos A-\sin B\cos B}=\] [MP PET 1993]
  A)
  \[\tan (A-B)\] done clear
  B)
  \[\tan (A+B)\] done clear
  C)
  \[\cot (A-B)\] done clear
  D)
  \[\cot (A+B)\] done clear
  View Solution play_arrow

• question_answer20)
  If \[\cos (\alpha +\beta )=\frac{4}{5},\sin (\alpha -\beta )=\frac{5}{13}\] and \[\alpha ,\beta \] lie between 0 and \[\frac{\pi }{4},\]then \[\tan 2\alpha =\] [IIT 1979; EAMCET 2002]
  A)
  \[\frac{16}{63}\] done clear
  B)
  \[\frac{56}{33}\] done clear
  C)
  \[\frac{28}{33}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer21)
  If \[\cos \theta =\frac{8}{17}\] and \[\theta \] lies in the 1st quadrant, then the value of \[\cos (30{}^\circ +\theta )+\cos (45{}^\circ -\theta )+\cos (120{}^\circ -\theta )\] is
  A)
  \[\frac{23}{17}\left( \frac{\sqrt{3}-1}{2}+\frac{1}{\sqrt{2}} \right)\] done clear
  B)
  \[\frac{23}{17}\left( \frac{\sqrt{3}+1}{2}+\frac{1}{\sqrt{2}} \right)\] done clear
  C)
  \[\frac{23}{17}\left( \frac{\sqrt{3}-1}{2}-\frac{1}{\sqrt{2}} \right)\] done clear
  D)
  \[\frac{23}{17}\left( \frac{\sqrt{3}+1}{2}-\frac{1}{\sqrt{2}} \right)\] done clear
  View Solution play_arrow

• question_answer22)
  If \[\tan x+\tan \left( \frac{\pi }{3}+x \right)+\tan \left( \frac{2\pi }{3}+x \right)=3,\] then
  A)
  \[\tan x=1\] done clear
  B)
  \[\tan 2x=1\] done clear
  C)
  \[\tan 3x=1\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer23)
  The value of \[\sin {{47}^{o}}+\sin 61{}^\circ -\sin 11{}^\circ -\sin 25{}^\circ =\] [MP PET 2001; EAMCET 2003]
  A)
  \[\sin 36{}^\circ \] done clear
  B)
  \[\cos 36{}^\circ \] done clear
  C)
  \[\sin 7{}^\circ \] done clear
  D)
  \[\cos 7{}^\circ \] done clear
  View Solution play_arrow

• question_answer24)
  If \[\sin (\theta +\alpha )=a\] and \[\sin (\theta +\beta )=b,\] then \[\cos 2\,(\alpha -\beta )-4ab\,\cos (\alpha -\beta )\] is equal to
  A)
  \[1-{{a}^{2}}-{{b}^{2}}\] done clear
  B)
  \[1-2{{a}^{2}}-2{{b}^{2}}\] done clear
  C)
  \[2+{{a}^{2}}+{{b}^{2}}\] done clear
  D)
  \[2-{{a}^{2}}-{{b}^{2}}\] done clear
  View Solution play_arrow

• question_answer25)
  The expression\[{{\cos }^{2}}(A-B)+{{\cos }^{2}}B-2\cos (A-B)\cos A\cos B\]  is 
  A)
  Dependent on B done clear
  B)
  Dependent on A and B done clear
  C)
  Dependent on A done clear
  D)
  Independent of A and B done clear
  View Solution play_arrow

• question_answer26)
  The value of \[\cos 15{}^\circ -\sin 15{}^\circ \]is equal to [MNR 1975; MP PET 1994, 2002]
  A)
  \[\frac{1}{\sqrt{2}}\] done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[-\frac{1}{\sqrt{2}}\] done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer27)
  If \[\tan \alpha ,\tan \beta \]are the roots of the equation \[{{x}^{2}}+px+q=0\text{  }(p\ne 0),\] then
  A)
  \[{{\sin }^{2}}(\alpha +\beta )+p\sin (\alpha +\beta )\cos (\alpha +\beta )+q{{\cos }^{2}}(\alpha +\beta )=q\] done clear
  B)
  \[\tan (\alpha +\beta )=\frac{p}{q-1}\] done clear
  C)
  \[\cos (\alpha +\beta )=1-q\] done clear
  D)
  \[\sin (\alpha +\beta )=-p\] done clear
  View Solution play_arrow

• question_answer28)
  \[\tan 5x\tan 3x\tan 2x=\] [EAMCET 1991]
  A)
  \[\tan 5x-\tan 3x-\tan 2x\] done clear
  B)
  \[\frac{\sin 5x-\sin 3x-\sin 2x}{\cos 5x-\cos 3x-\cos 2x}\] done clear
  C)
  0 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer29)
  If \[\tan \alpha \] equals the integral solution of the inequality \[4{{x}^{2}}-16x+15<0\] and \[\cos \beta \] equals to the slope of the bisector of first quadrant, then \[\sin (\alpha +\beta )\sin (\alpha -\beta )\]is equal to [Kerala (Engg.) 1993]
  A)
  \[\frac{3}{5}\] done clear
  B)
  \[-\frac{3}{5}\] done clear
  C)
  \[\frac{2}{\sqrt{5}}\] done clear
  D)
  \[\frac{4}{5}\] done clear
  View Solution play_arrow

• question_answer30)
  \[\tan \frac{2\pi }{5}-\tan \frac{\pi }{15}-\sqrt{3}\tan \frac{2\pi }{5}\tan \frac{\pi }{15}\] is equal to
  A)
  \[-\sqrt{3}\] done clear
  B)
  \[\frac{1}{\sqrt{3}}\] done clear
  C)
  1 done clear
  D)
  \[\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer31)
  The value of  \[\cos 12{}^\circ +\cos 84{}^\circ +\cos 156{}^\circ +\cos 132{}^\circ \] is [Kerala (Engg.) 1993]
  A)
  \[\frac{1}{2}\] done clear
  B)
  1 done clear
  C)
  \[-\frac{1}{2}\] done clear
  D)
  \[\frac{1}{8}\] done clear
  View Solution play_arrow

• question_answer32)
  The value of \[\cos 52{}^\circ +\cos 68{}^\circ +\cos 172{}^\circ \] is [MP PET 1997; Pb. CET 1995, 99]
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  \[\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer33)
  \[\frac{\cos 17{}^\circ +\sin 17{}^\circ }{\cos 17{}^\circ -\sin 17{}^\circ }=\]      [MP PET 1998]
  A)
  \[\tan 62{}^\circ \] done clear
  B)
  \[\tan 56{}^\circ \] done clear
  C)
  \[\tan 54{}^\circ \] done clear
  D)
  \[\tan 73{}^\circ \] done clear
  View Solution play_arrow

• question_answer34)
  \[\frac{\cos 9{}^\circ +\sin 9{}^\circ }{\cos 9{}^\circ -\sin 9{}^\circ }=\] [EAMCET 1992; Kerala (Engg.) 2005]
  A)
  \[\tan 54{}^\circ \] done clear
  B)
  \[\tan 36{}^\circ \] done clear
  C)
  \[\tan 18{}^\circ \] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer35)
  \[\frac{\sin 70{}^\circ +\cos 40{}^\circ }{\cos 70{}^\circ +\sin 40{}^\circ }=\] [CET 1986; MP PET 1999]
  A)
  1 done clear
  B)
  \[\frac{1}{\sqrt{3}}\] done clear
  C)
  \[\sqrt{3}\] done clear
  D)
  \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer36)
  If \[\cos (A-B)=\frac{3}{5}\] and \[\tan A\tan B=2,\] then [MP PET 1997]
  A)
  \[\cos A\cos B=\frac{1}{5}\] done clear
  B)
  \[\sin A\sin B=-\frac{2}{5}\] done clear
  C)
  \[\cos A\cos B=-\frac{1}{5}\] done clear
  D)
  \[\sin A\sin B=-\frac{1}{5}\] done clear
  View Solution play_arrow

• question_answer37)
  \[\tan 100{}^\circ +\tan 125{}^\circ +\tan 100{}^\circ \tan 125{}^\circ =\] [DCE 1999]
  A)
  0 done clear
  B)
  1/2 done clear
  C)
  -1 done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer38)
  If \[\frac{\pi }{2}<\alpha <\pi ,\,\text{ }\pi <\beta <\frac{3\pi }{2};\] \[\sin \alpha =\frac{15}{17}\] and \[\tan \beta =\frac{12}{5}\], then the value of \[\sin (\beta -\alpha )\] is [Roorkee 2000]
  A)
  -171/221 done clear
  B)
  -21/221 done clear
  C)
  21/221 done clear
  D)
  171/221  done clear
  View Solution play_arrow

• question_answer39)
  If \[\cos x+\cos y+\cos \alpha =0\] and \[\sin x+\sin y+\sin \alpha =0,\] then \[\cot \,\left( \frac{x+y}{2} \right)=\] [Karnataka CET 2001]
  A)
  \[\sin \alpha \] done clear
  B)
  \[\cos \alpha \] done clear
  C)
  \[\cot \alpha \] done clear
  D)
  \[\sin \,\left( \frac{x+y}{2} \right)\] done clear
  View Solution play_arrow

• question_answer40)
  If \[\sin \theta +\sin 2\theta +\sin 3\theta =\sin \alpha \]and \[\cos \theta +\cos 2\theta +\cos 3\theta =\cos \alpha \], then q  is equal to [AMU 2001]
  A)
  \[\alpha /2\] done clear
  B)
  \[\alpha \] done clear
  C)
  \[2\alpha \] done clear
  D)
  \[\alpha /6\] done clear
  View Solution play_arrow

• question_answer41)
  \[\frac{\cos {{10}^{o}}+\sin {{10}^{o}}}{\cos {{10}^{o}}-\sin {{10}^{o}}}=\] [MP PET 2002]
  A)
  \[\tan \,{{55}^{o}}\] done clear
  B)
  \[\cot {{55}^{o}}\] done clear
  C)
  \[-\tan {{35}^{o}}\] done clear
  D)
  \[-\cot {{35}^{o}}\] done clear
  View Solution play_arrow

• question_answer42)
  If \[\cos P=\frac{1}{7}\] and \[\cos Q=\frac{13}{14},\] where P and Q both are acute angles. Then the value of \[P-Q\] is [Karnataka CET 2002]
  A)
  \[{{30}^{o}}\] done clear
  B)
  \[{{60}^{o}}\] done clear
  C)
  \[{{45}^{o}}\] done clear
  D)
  \[{{75}^{o}}\] done clear
  View Solution play_arrow

• question_answer43)
  \[\sec {{50}^{o}}+\tan {{50}^{o}}\] is equal to [DCE 2002]
  A)
  \[\tan {{20}^{o}}+\tan {{50}^{o}}\] done clear
  B)
  \[2\tan {{20}^{o}}+\tan {{50}^{o}}\] done clear
  C)
  \[\tan {{20}^{o}}+2\tan {{50}^{o}}\] done clear
  D)
  \[2\tan {{20}^{o}}+2\tan {{50}^{o}}\] done clear
  View Solution play_arrow

• question_answer44)
  If \[\tan \alpha ={{(1+{{2}^{-x}})}^{-1}},\] \[\tan \beta ={{(1+{{2}^{x+1}})}^{-1}}\], then \[\alpha +\beta \] equals [AMU 2002]
  A)
  \[\pi /6\] done clear
  B)
  \[\pi /4\] done clear
  C)
  \[\pi /3\] done clear
  D)
  \[\pi /2\] done clear
  View Solution play_arrow

• question_answer45)
  The sum \[S=\sin \theta +\sin 2\,\theta +....+\sin \,n\theta ,\] equals  [AMU 2002]
  A)
  \[\sin \frac{1}{2}(n+1)\text{ }\theta \sin \frac{1}{2}n\text{ }\theta /\sin \frac{\theta }{2}\] done clear
  B)
  \[\cos \frac{1}{2}(n+1)\text{ }\theta \sin \frac{1}{2}n\theta /\sin \frac{\theta }{2}\] done clear
  C)
  \[\sin \frac{1}{2}(n+1)\theta \cos \frac{1}{2}n\theta /\sin \frac{\theta }{2}\] done clear
  D)
  \[\cos \frac{1}{2}(n+1)\theta \cos \frac{1}{2}n\theta /\sin \frac{\theta }{2}\]    done clear
  View Solution play_arrow

• question_answer46)
  The value of \[\cot {{70}^{o}}+4\cos {{70}^{o}}\] is [Orissa JEE 2003]
  A)
  \[\frac{1}{\sqrt{3}}\] done clear
  B)
  \[\sqrt{3}\] done clear
  C)
  \[2\sqrt{3}\] done clear
  D)
  \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer47)
  The expression \[2\cos \frac{\pi }{13}.\cos \frac{9\pi }{13}+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13}\] is equal to [UPSEAT 2004]
  A)
  -1 done clear
  B)
  0 done clear
  C)
  1 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer48)
  If \[\sin \theta =\frac{12}{13},(0<\theta <\frac{\pi }{2})\] and \[\cos \varphi =-\frac{3}{5},\left( \pi <\varphi <\frac{3\pi }{2} \right)\]. Then \[\sin (\theta +\varphi )\]will be [Orissa JEE 2004]
  A)
  \[\frac{-56}{61}\] done clear
  B)
  \[\frac{-56}{65}\] done clear
  C)
  \[\frac{1}{65}\] done clear
  D)
  -56 done clear
  View Solution play_arrow

• question_answer49)
  If \[\tan A-\tan B=x\] and \[\cot B-\cot A=y,\]then \[\cot (A-B)=\]
  A)
  \[\frac{1}{x}+y\] done clear
  B)
  \[\frac{1}{xy}\] done clear
  C)
  \[\frac{1}{x}-\frac{1}{y}\] done clear
  D)
  \[\frac{1}{x}+\frac{1}{y}\] done clear
  View Solution play_arrow

• question_answer50)
  \[\sin 12{}^\circ \sin 48{}^\circ \sin 54{}^\circ =\] [IIT 1982; Kerala (Engg.) 2001]
  A)
  1/16 done clear
  B)
  1/32 done clear
  C)
  1/8 done clear
  D)
  1/4 done clear
  View Solution play_arrow

• question_answer51)
  \[\cos \frac{\pi }{5}\cos \frac{2\pi }{5}\cos \frac{4\pi }{5}\cos \frac{8\pi }{5}=\]
  A)
  1/16 done clear
  B)
  0 done clear
  C)
  - 1/8 done clear
  D)
  -1/16 done clear
  View Solution play_arrow

• question_answer52)
  \[\frac{\cos 12{}^\circ -\sin 12{}^\circ }{\cos 12{}^\circ +\sin 12{}^\circ }+\frac{\sin 147{}^\circ }{\cos 147{}^\circ }=\] [MP PET 1991]
  A)
  1 done clear
  B)
  -1 done clear
  C)
  0 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer53)
  \[\tan 20{}^\circ \tan 40{}^\circ \tan 60{}^\circ \tan 80{}^\circ =\] [IIT 1974]
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  \[\sqrt{3}/2\] done clear
  View Solution play_arrow

• question_answer54)
  \[\cos 20{}^\circ \cos 40{}^\circ \cos 80{}^\circ =\] [MP PET 1989]
  A)
  1/2 done clear
  B)
  1/4 done clear
  C)
  1/6 done clear
  D)
  1/8 done clear
  View Solution play_arrow

• question_answer55)
  \[\sin 36{}^\circ \sin 72{}^\circ \sin 108{}^\circ \sin 144{}^\circ =\] [IIT 1965]
  A)
  1/4 done clear
  B)
  1/16 done clear
  C)
  3/4 done clear
  D)
  5/16 done clear
  View Solution play_arrow

• question_answer56)
  If \[\cos A=m\cos B,\]then [MNR 1990]
  A)
  \[\cot \frac{A+B}{2}=\frac{m+1}{m-1}\tan \frac{B-A}{2}\] done clear
  B)
  \[\tan \frac{A+B}{2}=\frac{m+1}{m-1}\cot \frac{B-A}{2}\] done clear
  C)
  \[\cot \frac{A+B}{2}=\frac{m+1}{m-1}\tan \frac{A-B}{2}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer57)
  If \[x=\cos 10{}^\circ \cos 20{}^\circ \cos 40{}^\circ ,\]then the value of \[x\] is  [Roorkee 1995]
  A)
  \[\frac{1}{4}\tan 10{}^\circ \] done clear
  B)
  \[\frac{1}{8}\cot 10{}^\circ \] done clear
  C)
  \[\frac{1}{8}\text{cosec}10{}^\circ \] done clear
  D)
  \[\frac{1}{8}\sec 10{}^\circ \] done clear
  View Solution play_arrow

• question_answer58)
  \[\sin 12{}^\circ \sin 24{}^\circ \sin 48{}^\circ \sin 84{}^\circ =\] [EAMCET 1989]
  A)
  \[\cos 20{}^\circ \cos 40{}^\circ \cos 60{}^\circ \cos 80{}^\circ \] done clear
  B)
  \[\sin 20{}^\circ \sin 40{}^\circ \sin 60{}^\circ \sin 80{}^\circ \] done clear
  C)
  \[\frac{3}{15}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer59)
  \[\tan 3A-\tan 2A-\tan A=\] [MNR 1982; Pb. CET 1991]
  A)
  \[\tan 3A\tan 2A\tan A\] done clear
  B)
  \[-\tan 3A\tan 2A\tan A\] done clear
  C)
  \[\tan A\tan 2A-\tan 2A\tan 3A-\tan 3A\tan A\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer60)
  \[{{\cos }^{2}}\left( \frac{\pi }{4}-\beta  \right)-{{\sin }^{2}}\left( \alpha -\frac{\pi }{4} \right)=\]
  A)
  \[\sin (\alpha +\beta )\sin (\alpha -\beta )\] done clear
  B)
  \[\cos (\alpha +\beta )\cos (\alpha -\beta )\] done clear
  C)
  \[\sin (\alpha -\beta )\cos (\alpha +\beta )\] done clear
  D)
  \[\sin (\alpha +\beta )\cos (\alpha -\beta )\] done clear
  View Solution play_arrow

• question_answer61)
  \[\tan 9{}^\circ -\tan 27{}^\circ -\tan 63{}^\circ +\tan 81{}^\circ =\] [Roorkee 1989]
  A)
  1/2 done clear
  B)
  2 done clear
  C)
  4 done clear
  D)
  8 done clear
  View Solution play_arrow

• question_answer62)
  \[\frac{\sin 3\theta +\sin 5\theta +\sin 7\theta +\sin 9\theta }{\cos 3\theta +\cos 5\theta +\cos 7\theta +\cos 9\theta }=\] [Roorkee 1973]
  A)
  \[\tan 3\theta \] done clear
  B)
  \[\cot 3\theta \] done clear
  C)
  \[\tan 6\theta \] done clear
  D)
  \[\cot 6\theta \] done clear
  View Solution play_arrow

• question_answer63)
  \[\sin {{163}^{o}}\cos {{347}^{o}}+\sin {{73}^{o}}\sin {{167}^{o}}=\] [MP PET 2000]
  A)
  0 done clear
  B)
  1/2 done clear
  C)
  1 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer64)
  The value of \[\sin 600{}^\circ \cos 330{}^\circ +\cos 120{}^\circ \sin 150{}^\circ \] is  [MP PET 1994]
  A)
  -1 done clear
  B)
  1 done clear
  C)
  \[\frac{1}{\sqrt{2}}\] done clear
  D)
  \[\frac{\sqrt{3}}{2}\] done clear
  View Solution play_arrow

• question_answer65)
  \[\cos A+\cos (240{}^\circ +A)+\cos (240{}^\circ -A)=\] [MP PET 1991]
  A)
  \[\cos A\] done clear
  B)
  0 done clear
  C)
  \[\sqrt{3}\sin A\] done clear
  D)
  \[\sqrt{3}\cos A\] done clear
  View Solution play_arrow

• question_answer66)
  \[{{\cos }^{2}}\left( \frac{\pi }{6}+\theta  \right)-{{\sin }^{2}}\left( \frac{\pi }{6}-\theta  \right)=\] [EAMCET 2001]
  A)
  \[\frac{1}{2}\cos 2\theta \] done clear
  B)
  0 done clear
  C)
  \[-\frac{1}{2}\cos 2\,\theta \] done clear
  D)
  \[\frac{1}{2}\]        done clear
  View Solution play_arrow

• question_answer67)
  If \[b\sin \alpha =a\sin (\alpha +2\beta ),\] then \[\frac{a+b}{a-b}=\]
  A)
  \[\frac{\tan \beta }{\tan (\alpha +\beta )}\] done clear
  B)
  \[\frac{\cot \beta }{\cot (\alpha -\beta )}\] done clear
  C)
  \[\frac{-\cot \beta }{\cot (\alpha +\beta )}\] done clear
  D)
  \[\frac{\cot \beta }{\cot (\alpha +\beta )}\] done clear
  View Solution play_arrow

• question_answer68)
  \[\frac{\sin (B+A)+\cos (B-A)}{\sin (B-A)+\cos (B+A)}=\] [Roorkee 1970; IIT 1966]
  A)
  \[\frac{\cos B+\sin B}{\cos B-\sin B}\] done clear
  B)
  \[\frac{\cos A+\sin A}{\cos A-\sin A}\] done clear
  C)
  \[\frac{\cos A-\sin A}{\cos A+\sin A}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer69)
  If \[\frac{\sin (x+y)}{\sin (x-y)}=\frac{a+b}{a-b},\]then \[\frac{\tan x}{\tan y}\] is equal to
  A)
  \[\frac{b}{a}\] done clear
  B)
  \[\frac{a}{b}\] done clear
  C)
  \[ab\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer70)
  If \[\sin A+\sin 2A=x\] and \[\cos A+\cos 2A=y,\] then \[({{x}^{2}}+{{y}^{2}})({{x}^{2}}+{{y}^{2}}-3)=\]
  A)
  \[2y\] done clear
  B)
  \[y\] done clear
  C)
  \[3y\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer71)
  The expression \[\frac{\cos 6x+6\cos 4x+15\cos 2x+10}{\cos 5x+5\cos 3x+10\cos x}\] is equal to
  A)
  \[\cos 2x\] done clear
  B)
  \[2\cos x\] done clear
  C)
  \[{{\cos }^{2}}x\] done clear
  D)
  \[1+\cos x\] done clear
  View Solution play_arrow

• question_answer72)
  \[\cos \alpha .\sin (\beta -\gamma )+\cos \beta .\sin (\gamma -\alpha )+\cos \gamma .\sin (\alpha -\beta )=\] [EAMCET 2003]
  A)
  0 done clear
  B)
  1/2 done clear
  C)
  1 done clear
  D)
  \[4\cos \alpha \cos \beta \cos \gamma \] done clear
  View Solution play_arrow

• question_answer73)
  \[\sin (\beta +\gamma -\alpha )+\sin (\gamma +\alpha -\beta )\]\[+\sin (\alpha +\beta -\gamma )-\sin (\alpha +\beta +\gamma )=\]
  A)
  \[2\sin \alpha \sin \beta \sin \gamma \] done clear
  B)
  \[4\sin \alpha \sin \beta \sin \gamma \] done clear
  C)
  \[\sin \alpha \sin \beta \sin \gamma \] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer74)
  If \[m\tan (\theta -30{}^\circ )=n\tan (\theta +120{}^\circ ),\] then \[\frac{m+n}{m-n}=\] [IIT 1966]
  A)
  \[2\,\cos \,2\theta \] done clear
  B)
  \[\cos \,\,2\theta \] done clear
  C)
  \[2\,\sin \,2\theta \] done clear
  D)
  \[\sin \,\,2\theta \] done clear
  View Solution play_arrow

• question_answer75)
  \[2\cos x-\cos 3x-\cos 5x=\] [Roorkee 1974]
  A)
  \[16{{\cos }^{3}}x{{\sin }^{2}}x\] done clear
  B)
  \[16{{\sin }^{3}}x{{\cos }^{2}}x\] done clear
  C)
  \[4{{\cos }^{3}}x{{\sin }^{2}}x\] done clear
  D)
  \[4{{\sin }^{3}}x{{\cos }^{2}}x\] done clear
  View Solution play_arrow

• question_answer76)
  \[1+\cos 2x+\cos 4x+\cos 6x=\] [Roorkee 1974]
  A)
  \[2\cos x\cos 2x\cos 3x\] done clear
  B)
  \[4\sin x\,\cos 2x\cos 3x\] done clear
  C)
  \[4\cos x\cos 2x\cos 3x\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer77)
  If \[\frac{\sin A-\sin C}{\cos C-\cos A}=\cot B,\] then A,B,C are in
  A)
  A.P. done clear
  B)
  G.P. done clear
  C)
  H.P. done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer78)
  \[\cos \frac{2\pi }{15}\cos \frac{4\pi }{15}\cos \frac{8\pi }{15}\cos \frac{16\pi }{15}\] = [IIT 1985]
  A)
  1/2 done clear
  B)
  1/4 done clear
  C)
  1/8 done clear
  D)
  1/16 done clear
  View Solution play_arrow

• question_answer79)
  The value of \[{{\cos }^{2}}\frac{\pi }{12}+{{\cos }^{2}}\frac{\pi }{4}+{{\cos }^{2}}\frac{5\pi }{12}\] is [Karnataka CET 2002]
  A)
  \[\frac{3}{2}\] done clear
  B)
  \[\frac{2}{3}\] done clear
  C)
  \[\frac{3+\sqrt{3}}{2}\] done clear
  D)
  \[\frac{2}{3+\sqrt{3}}\] done clear
  View Solution play_arrow

• question_answer80)
  The value of \[\sin \frac{\pi }{16}\sin \frac{3\pi }{16}\sin \frac{5\pi }{16}\sin \frac{7\pi }{16}\]is [MP PET 2004]
  A)
  \[\frac{1}{16}\] done clear
  B)
  \[\frac{\sqrt{2}}{16}\] done clear
  C)
  \[\frac{1}{8}\] done clear
  D)
  \[\frac{\sqrt{2}}{8}\] done clear
  View Solution play_arrow

• question_answer81)
  \[{{\cos }^{2}}{{76}^{o}}+{{\cos }^{2}}{{16}^{o}}-\cos {{76}^{o}}\cos {{16}^{o}}=\] [EAMCET 2002]
  A)
  -1/4 done clear
  B)
  1/2 done clear
  C)
  0 done clear
  D)
  3/4    done clear
  View Solution play_arrow

• question_answer82)
  \[\cos \frac{\pi }{7}\cos \frac{2\pi }{7}\cos \frac{4\pi }{7}=\] [MP PET 1998]
  A)
  0 done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[\frac{1}{4}\] done clear
  D)
  \[-\frac{1}{8}\] done clear
  View Solution play_arrow

• question_answer83)
  The value of \[\frac{\tan {{70}^{o}}-\tan {{20}^{o}}}{\tan {{50}^{o}}}=\] [Karnataka CET 2003]
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer84)
  \[{{\cos }^{2}}\alpha +{{\cos }^{2}}(\alpha +120{}^\circ )+{{\cos }^{2}}(\alpha -120{}^\circ )\] is equal to   [MP PET 1993]
  A)
  3/2 done clear
  B)
  1 done clear
  C)
  1/2 done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer85)
  The value of \[\tan {{20}^{o}}+2\tan {{50}^{o}}-\tan {{70}^{o}}\]is equal to [AMU 2005]
  A)
  1 done clear
  B)
  0 done clear
  C)
  \[\tan {{50}^{o}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow