10th Class Mathematics Introduction to Trigonometry Question Bank

done Introduction to Trigonometery Total Questions - 58

• question_answer1)
  \[\Delta ABC\]is right angled at A. If AC = 8 cm and AB = 6 cm, what is the value of cosec B?
  A)
   \[\frac{5}{4}\]                                                   done clear
  B)
   \[\frac{3}{4}\]   done clear
  C)
   \[\frac{4}{3}\]                                   done clear
  D)
          \[\frac{4}{5}\] done clear
  View Solution play_arrow

• question_answer2)
  \[\Delta ABC\]is right angled at A .lf\[BC=\sqrt{2}\]and AB = AC =1, what is the measure of\[\angle B\]?
  A)
   \[\text{6}0{}^\circ \]                                      done clear
  B)
   \[\text{45}{}^\circ \] done clear
  C)
   \[\text{3}0{}^\circ \]                      done clear
  D)
          \[\text{9}0{}^\circ \] done clear
  View Solution play_arrow

• question_answer3)
  What is the value of\[\theta \]tor which\[\tan \theta =\cot \theta \]?
  A)
   \[\text{6}0{}^\circ \]                      done clear
  B)
   \[\text{45}{}^\circ \]  done clear
  C)
   \[\text{9}0{}^\circ \]      done clear
  D)
          \[0{}^\circ \] done clear
  View Solution play_arrow

• question_answer4)
  Given\[\sin \theta +\frac{1}{\sin \theta }=4\], what is the value
  A)
   20                          done clear
  B)
          16   done clear
  C)
   14                                          done clear
  D)
   4 done clear
  View Solution play_arrow

• question_answer5)
  Given\[{{\sin }^{2}}\theta +\frac{1}{{{\sin }^{2}}\theta }\], what is the value of \[\sin \theta +\cos \theta \]?
  A)
   \[\frac{25}{31}\]              done clear
  B)
          \[\frac{31}{25}\]  done clear
  C)
   \[\frac{24}{25}\]              done clear
  D)
          \[\frac{31}{24}\] done clear
  View Solution play_arrow

• question_answer6)
  Find the value of \[\text{cos3}0{}^\circ \text{ cos45}{}^\circ \text{ }-\text{ sin3}0{}^\circ \text{ sin45}{}^\circ \].
  A)
   \[\frac{\sqrt{6}+1}{2}\]                done clear
  B)
   \[\frac{\sqrt{6}+\sqrt{2}}{4}\] done clear
  C)
   \[\frac{\sqrt{6}-\sqrt{2}}{8}\]    done clear
  D)
          \[\frac{\sqrt{2}(\sqrt{3}-1)}{4}\] done clear
  View Solution play_arrow

• question_answer7)
  What is the value of\[\text{tan 7}{}^\circ \text{ tan 23}{}^\circ \text{ tan 6}0{}^\circ \text{ tan 67}{}^\circ \text{ tan 83}{}^\circ \]?
  A)
   \[\frac{1}{\sqrt{3}}\]                                     done clear
  B)
   \[\sqrt{3}\]  done clear
  C)
   1                             done clear
  D)
          \[\propto \] done clear
  View Solution play_arrow

• question_answer8)
  \[\Delta \text{ABC}\]is an isosceles triangle with the unequal side measuring 12 cm. If both the equal sides measure 19 cm, what is the measure of\[\angle \text{BAC}\]?
  A)
   \[\text{36}.\text{8}{}^\circ \]                                    done clear
  B)
   \[\text{68}{}^\circ \] done clear
  C)
   \[\text{38}{}^\circ \]                      done clear
  D)
          \[\text{6}0{}^\circ \] done clear
  View Solution play_arrow

• question_answer9)
  \[\text{ABCD}\] is a trapezium in which AB = 8 cm, AD = 4 cm and CD = 3 cm. What is the length of BC to the nearest whole number?
  A)
   5 cm                      done clear
  B)
          \[\sqrt{41}\,cm\] done clear
  C)
   8 cm                      done clear
  D)
          7 cm done clear
  View Solution play_arrow

• question_answer10)
  The figure shows an isosceles triangle ABC. Find the length of the perpendicular from A to BC.
  A)
   5.45 cm                                done clear
  B)
   4.55 cm done clear
  C)
   5.6 cm                  done clear
  D)
          4.54 cm done clear
  View Solution play_arrow

• question_answer11)
  If \[\text{sec}\theta =\text{2p}\] and \[\tan \theta =\frac{\text{2}}{p}\] find the value\[2\left( {{p}^{2}}-\frac{1}{{{p}^{2}}} \right)\].
  A)
   \[\frac{1}{2}\]   done clear
  B)
                          \[\frac{1}{\sqrt{2}}\] done clear
  C)
   \[\frac{1}{4}\]                   done clear
  D)
          \[\frac{1}{8}\] done clear
  View Solution play_arrow

• question_answer12)
  What is the value of\[\theta \]if\[\sqrt{3}\tan 2\theta -3=0\]?
  A)
   \[\text{45}{}^\circ \]                                      done clear
  B)
  \[\text{9}0{}^\circ \] done clear
  C)
   \[\text{3}0{}^\circ \]      done clear
  D)
         \[\text{6}0{}^\circ \] done clear
  View Solution play_arrow

• question_answer13)
  Given\[\sin \theta +\cos \theta =\sqrt{3}\], what is the value of\[\tan \theta +\cot \theta \]?
  A)
   \[\frac{1}{\sqrt{2}}\]                                     done clear
  B)
   \[\frac{2}{\sqrt{3}}\] done clear
  C)
   \[\frac{\sqrt{3}}{2}\]                     done clear
  D)
          1 done clear
  View Solution play_arrow

• question_answer14)
  If \[\frac{\tan {{26}^{o}}+\tan {{19}^{o}}}{x(1-\tan {{26}^{o}}\tan {{19}^{o}})}=\cos {{60}^{o}}\], what is the value of \[x\]?
  A)
   1                                             done clear
  B)
   \[\sqrt{2}\]  done clear
  C)
   2                             done clear
  D)
          \[\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer15)
  If \[\sin 2\left( \frac{2}{1}.\frac{3}{2}.\frac{4}{3}....\frac{x-1}{x-2} \right)=1,\]\[0<x<100\], find the value of \[x\].
  A)
   \[\text{91}{}^\circ \]                      done clear
  B)
   \[\text{8}0{}^\circ \]  done clear
  C)
   \[\text{49}{}^\circ \]                      done clear
  D)
   \[\text{46}{}^\circ \] done clear
  View Solution play_arrow

• question_answer16)
  What is the angle between the hour and minute hands of a clock at 02 :15 hours?
  A)
   \[\text{15}{}^\circ \]      done clear
  B)
                          \[7\frac{{{1}^{o}}}{2}\] done clear
  C)
   \[22\frac{{{1}^{o}}}{2}\]               done clear
  D)
          \[\text{3}0{}^\circ \] done clear
  View Solution play_arrow

• question_answer17)
  C is the centre of a circle of radius 3 units, and \[\theta \]is the angle as shown in the given figure. If \[\sin \theta +{{\cos }^{2}}\theta =\frac{{{x}^{2}}+1}{{{x}^{2}}}\],find the value of x.
  A)
   2                                             done clear
  B)
   4    done clear
  C)
   6                             done clear
  D)
          8 done clear
  View Solution play_arrow

• question_answer18)
  If\[\tan \theta +\sec \theta =2\], \[0\le \theta \le \frac{\pi }{2}\]find the value of the\[\tan \theta \].
  A)
   \[\frac{3}{4}\]                                                   done clear
  B)
   \[\frac{5}{4}\]   done clear
  C)
   \[\frac{3}{2}\]                                   done clear
  D)
          \[\frac{5}{2}\] done clear
  View Solution play_arrow

• question_answer19)
  Graphs of \[y=\sin x\] and\[y=\cos x\], where \[0\le x\le \frac{\pi }{2}\]intersect at a point. Find abscissa.
  A)
    \[\frac{\pi }{6}\]                             done clear
  B)
   \[\frac{\pi }{4}\]    done clear
  C)
   \[\frac{\pi }{3}\]              done clear
  D)
          0 done clear
  View Solution play_arrow

• question_answer20)
  Find the value of\[\text{sin 15}{}^\circ \].
  A)
   \[\frac{\sqrt{3}+1}{\sqrt{2}}\]   done clear
  B)
          \[\frac{\sqrt{3}-1}{\sqrt{2}}\] 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_answer21)
  What is the value of \[~\text{sin}0{}^\circ +\text{cos3}0{}^\circ -\text{tan45}{}^\circ +\] \[\text{cosec 6}0{}^\circ \text{ }+\text{ cot9}0{}^\circ \]?
  A)
   \[\frac{7\sqrt{3}-6}{6}\]               done clear
  B)
          \[\frac{6+7\sqrt{3}}{6}\] done clear
  C)
   0                             done clear
  D)
          2 done clear
  View Solution play_arrow

• question_answer22)
  If\[\sin \theta =-\frac{1}{2}\], what are the respective possible values of 9 between 0 and\[2\pi \]?
  A)
   \[\text{21}0{}^\circ \]and\[\text{3}00{}^\circ \]                done clear
  B)
   \[\text{24}0{}^\circ \]and \[\text{33}0{}^\circ \] done clear
  C)
   \[\text{24}0{}^\circ \]and\[\text{3}00{}^\circ \] done clear
  D)
          \[\text{21}0{}^\circ \]and\[\text{33}0{}^\circ \] done clear
  View Solution play_arrow

• question_answer23)
  In terms of radians what is the equivalent of\[\text{45}{}^\circ \]?
  A)
   \[25\pi \]            done clear
  B)
          \[0.25\pi \] done clear
  C)
   \[\frac{{{180}^{o}}\pi }{{{45}^{o}}}\]      done clear
  D)
          \[\frac{{{45}^{o}}}{\pi }\] done clear
  View Solution play_arrow

• question_answer24)
  Find the value of\[\sqrt{\frac{1-\cos A}{1+\cos A}}\]
  A)
   \[\text{sec A}-\text{cot A}\]      done clear
  B)
   \[\text{cosec A}-\text{cot A}\] done clear
  C)
   0                             done clear
  D)
          1 done clear
  View Solution play_arrow

• question_answer25)
  Find the value of\[\frac{5\cos \alpha -4}{3-5\sin \alpha }-\frac{3+5\sin \alpha }{4+5\cos \alpha }\]
  A)
   - 1                                          done clear
  B)
   5   done clear
  C)
   1                             done clear
  D)
          0 done clear
  View Solution play_arrow

• question_answer26)
  If\[x=3\cos A\cos B,y=3\cos A\sin B\]and \[\text{z}=\text{3 sin A}\], find the value of \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\].
  A)
   3                                             done clear
  B)
   6    done clear
  C)
   12                          done clear
  D)
          9 done clear
  View Solution play_arrow

• question_answer27)
  Find the value of \[\frac{1+\tan {{75}^{o}}}{1-\tan {{75}^{o}}}\]
  A)
   \[-\frac{2}{\sqrt{3}}\]                    done clear
  B)
   \[\sqrt{3}\] done clear
  C)
   \[-\sqrt{3}\]                      done clear
  D)
   \[\frac{1}{\sqrt{3}}\] done clear
  View Solution play_arrow

• question_answer28)
  If 8 tan A =15, find the value of\[\frac{\text{sinA}-\text{cosA}}{\text{sinA}+\text{cosA}}\]
  A)
  \[\frac{7}{23}\]                                 done clear
  B)
   \[\frac{11}{23}\] done clear
  C)
   \[\frac{13}{23}\]                              done clear
  D)
          \[\frac{17}{23}\] done clear
  View Solution play_arrow

• question_answer29)
  If\[4\sin \theta =3\cos \theta \],find\[\frac{{{\sec }^{2}}\theta }{4(1-{{\tan }^{2}}\theta )}\].
  A)
   \[\frac{25}{16}\]                              done clear
  B)
          \[\frac{25}{28}\] done clear
  C)
   \[\frac{1}{4}\]                   done clear
  D)
          \[\frac{5}{6}\] done clear
  View Solution play_arrow

• question_answer30)
  Find the value of\[\text{cos}{{\text{1}}^{o}}\text{cos2}{}^\circ \text{cos3}{}^\circ .....\text{cos89}{}^\circ \text{cos9}{{0}^{o}}\].
  A)
   1                             done clear
  B)
          \[\frac{1}{2}\]    done clear
  C)
   \[\frac{1}{\sqrt{2}}\]                     done clear
  D)
          0 done clear
  View Solution play_arrow

• question_answer31)
  If \[\tan x=\frac{x}{y}\], where x and y are whole numbers, find sin\[x\].
  A)
   \[\frac{y}{\sqrt{{{y}^{2}}-{{x}^{2}}}}\]   done clear
  B)
          \[\frac{x}{\sqrt{{{x}^{2}}+{{y}^{2}}}}\] done clear
  C)
   \[\frac{y}{\sqrt{{{x}^{2}}+{{y}^{2}}}}\]  done clear
  D)
          \[\frac{x}{\sqrt{{{y}^{2}}-{{x}^{2}}}}\] done clear
  View Solution play_arrow

• question_answer32)
  Find\[\frac{{{\sin }^{3}}\varphi +{{\cos }^{3}}\varphi }{\sin \varphi +\cos \varphi }\]
  A)
   \[\text{1 }+\text{sin}\varphi \text{ cos}\varphi \]            done clear
  B)
   \[\text{1}-\text{sinc}\varphi \text{ cos}\varphi \] done clear
  C)
   \[\text{1}-\text{sin}\varphi \text{ tan}\varphi \] done clear
  D)
          1 done clear
  View Solution play_arrow

• question_answer33)
  If \[x=\text{a sec}\theta +\text{b tan}\theta \] and\[\text{y}=\text{b sec}\theta +\text{a tan}\theta \], find\[{{x}^{2}}-{{y}^{2}}\].
  A)
   \[4ab\,\sec \theta +a\tan \theta \] done clear
  B)
          \[{{a}^{2}}-{{b}^{2}}\] done clear
  C)
   \[{{b}^{2}}-{{a}^{2}}\]   done clear
  D)
          \[{{a}^{2}}+{{b}^{2}}\] done clear
  View Solution play_arrow

• question_answer34)
  If\[\sec \theta +b\tan \theta =p\], what is the value of\[\cos \theta \]?
  A)
   \[\frac{{{p}^{2}}+1}{{{P}^{2}}-1}\]           done clear
  B)
          \[\frac{{{p}^{2}}-1}{{{({{P}^{2}}+1)}^{2}}}\] done clear
  C)
   \[\frac{2p}{{{P}^{2}}+1}\]            done clear
  D)
          \[\frac{4{{p}^{2}}}{{{({{P}^{2}}+1)}^{2}}}\] done clear
  View Solution play_arrow

• question_answer35)
  What is the numerical value of the expression \[\frac{\sin {{9}^{o}}}{\sin {{48}^{o}}}-\frac{\cos {{81}^{o}}}{\cos {{42}^{o}}}\]?
  A)
   1                             done clear
  B)
          \[\frac{1}{2}\]    done clear
  C)
   0                             done clear
  D)
          -1 done clear
  View Solution play_arrow

• question_answer36)
  Find the value of the expression \[[\cos ec({{75}^{o}}+\theta )-\sec ({{15}^{o}}-\theta )-\]\[\tan ({{55}^{o}}+\theta )+\cot ({{35}^{o}}-\theta )]\]
  A)
   - 1                                          done clear
  B)
   0    done clear
  C)
   1                                             done clear
  D)
   \[\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer37)
  If\[\cos (\alpha +\beta )=0\], what is the value of\[\sin (\alpha -\beta )\]?
  A)
   \[\cos \beta \]                  done clear
  B)
          \[\cos 2\beta \] done clear
  C)
   \[\sin \alpha \]                 done clear
  D)
          \[\sin 2\alpha \] done clear
  View Solution play_arrow

• question_answer38)
  If\[\cos 9\alpha =\sin \alpha \]a and\[9\alpha <{{90}^{o}}\], what is the value of tan 5 a?
  A)
   \[\frac{1}{\sqrt{3}}\]                     done clear
  B)
          \[\sqrt{3}\]   done clear
  C)
   1                             done clear
  D)
          \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer39)
  If\[\Delta \text{ABC}\]is right angled at C, find the value of\[\cos (A+B)\].
  A)
   0                             done clear
  B)
          1     done clear
  C)
   \[\frac{1}{2}\]                                   done clear
  D)
          \[\frac{\sqrt{3}}{2}\] done clear
  View Solution play_arrow

• question_answer40)
  If\[\text{sin A}+\text{sin2 A }=\text{ 1}\], find the value of the expression\[(\text{cos2 A}+\text{cos4 A})\].
  A)
   1                             done clear
  B)
          \[\frac{1}{2}\]    done clear
  C)
   2                             done clear
  D)
          3 done clear
  View Solution play_arrow

• question_answer41)
  Given that\[\text{sin}\alpha =\frac{1}{2}\text{and cos}\beta \text{=}\frac{1}{2}\], find the value of\[(\alpha +\beta )\].
  A)
   \[0{}^\circ \]                      done clear
  B)
          \[\text{3}0{}^\circ \]  done clear
  C)
   \[\text{6}0{}^\circ \]      done clear
  D)
          \[\text{9}0{}^\circ \] done clear
  View Solution play_arrow

• question_answer42)
  Find the value of the expression\[\frac{{{\sin }^{2}}{{22}^{o}}+{{\sin }^{2}}{{68}^{o}}}{{{\cos }^{2}}{{22}^{o}}+{{\cos }^{2}}{{68}^{o}}}+{{\sin }^{2}}{{63}^{o}}+\cos {{63}^{o}}\sin {{27}^{o}}\]
  A)
   3                                             done clear
  B)
   2    done clear
  C)
   1                             done clear
  D)
          0 done clear
  View Solution play_arrow

• question_answer43)
  If \[\sin \theta -\cos \theta =0\], find the value of \[({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )\]
  A)
   1                             done clear
  B)
          \[\frac{3}{4}\]    done clear
  C)
   \[\frac{1}{2}\]                                                   done clear
  D)
   \[\frac{1}{4}\] done clear
  View Solution play_arrow

• question_answer44)
  Find the value of \[\sin ({{45}^{o}}+\theta )-\cos ({{45}^{o}}-\theta )\].
  A)
   \[2\cos \theta \]              done clear
  B)
          0 done clear
  C)
   \[2\sin \theta \]               done clear
  D)
          1 done clear
  View Solution play_arrow

• question_answer45)
  What is the value of \[\text{si}{{\text{n}}^{\text{2}}}\text{5}{}^\circ +\text{si}{{\text{n}}^{\text{2}}}\text{1}0{}^\circ +\text{si}{{\text{n}}^{\text{2}}}\text{8}0{}^\circ +\text{si}{{\text{n}}^{\text{2}}}\text{85}{}^\circ \]?
  A)
   0                                             done clear
  B)
   1     done clear
  C)
   2                             done clear
  D)
          3 done clear
  View Solution play_arrow

• question_answer46)
  If \[\sin B=\frac{1}{2}\], find the value of\[\text{3cosB}-\text{4co}{{\text{s}}^{\text{3}}}\text{B}\].
  A)
   \[\frac{1}{2}\]                                                   done clear
  B)
   1     done clear
  C)
   2                             done clear
  D)
          0 done clear
  View Solution play_arrow

• question_answer47)
  If\[\tan x=\text{sin 45}{}^\circ \text{cos 45}{}^\circ +\text{sin3}0{}^\circ \], find the value of\[x\].
  A)
   \[{{30}^{o}}\]    done clear
  B)
         \[\text{6}0{}^\circ \]  done clear
  C)
   \[\text{45}{}^\circ \]                      done clear
  D)
  \[\text{9}0{}^\circ \] done clear
  View Solution play_arrow

• question_answer48)
  If \[\text{sin(A}+\text{B)}=\text{1}\]and\[\text{cos(A-B)}=\frac{\sqrt{3}}{2}\], find A and B.
  A)
   \[\text{45}{}^\circ ,\text{45}{}^\circ \]                  done clear
  B)
          \[\text{9}0{}^\circ ,\text{45}{}^\circ \] done clear
  C)
   \[\text{45}{}^\circ ,\text{ 3}0{}^\circ \]        done clear
  D)
   \[\text{6}0{}^\circ ,\text{ 3}0{}^\circ \] done clear
  View Solution play_arrow

• question_answer49)
  If\[4\tan \theta =1\], find the value of\[\frac{4\sin \theta -2\cos \theta }{4\sin \theta +3\cos \theta }\]
  A)
   \[\frac{1}{2}\]                                   done clear
  B)
          \[\frac{1}{6}\]    done clear
  C)
   \[\frac{2}{3}\]                                   done clear
  D)
          \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer50)
  If\[\sqrt{3}\tan \theta =3\sin \theta \], find the value of\[{{\sin }^{2}}\theta -{{\cos }^{2}}\theta \].
  A)
   \[\frac{\sqrt{2}}{\sqrt{3}}\]                                        done clear
  B)
   \[\frac{1}{3}\]    done clear
  C)
   \[\frac{1}{2}\]                                   done clear
  D)
          \[\frac{1}{\sqrt{3}}\] done clear
  View Solution play_arrow

• question_answer51)
  If \[\cos ec\theta =\frac{13}{12}\], find the value of\[\frac{2\sin \theta -3\cos \theta }{4\sin \theta -9\cos \theta }\]
  A)
   0                             done clear
  B)
   1     done clear
  C)
   3                             done clear
  D)
   2 done clear
  View Solution play_arrow

• question_answer52)
  Find the value \[\text{si}{{\text{n}}^{\text{2}}}\text{3}0{}^\circ \text{co}{{\text{s}}^{\text{2}}}\text{45}{}^\circ +\text{4ta}{{\text{n}}^{\text{2}}}\text{3}0{}^\circ \]\[+\frac{1}{2}{{\sin }^{2}}{{90}^{o}}-2{{\cos }^{2}}{{90}^{o}}+\frac{1}{24}\]
  A)
   1                                             done clear
  B)
   2    done clear
  C)
   \[\sqrt{2}\]        done clear
  D)
          \[\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer53)
  Find the value of\[\frac{2}{3}({{\cos }^{4}}{{30}^{o}}-{{\sin }^{4}}{{45}^{o}})\]\[-3({{\sin }^{2}}{{60}^{o}}-{{\sec }^{2}}{{45}^{o}})+\frac{1}{4}{{\cot }^{2}}{{30}^{o}}\]
  A)
   \[\frac{15}{4}\]                                done clear
  B)
   \[\frac{3}{4}\] done clear
  C)
   \[2\frac{65}{4}\]              done clear
  D)
          \[4\frac{17}{24}\] done clear
  View Solution play_arrow

• question_answer54)
  If \[\text{cos3x}=\text{cos 3}0{}^\circ \text{ sin 6}0{}^\circ \text{ }-\] \[\text{sin 3}0{}^\circ \text{ cos 6}0{}^\circ \] , find the value of x.
  A)
   \[\text{6}0{}^\circ \]                      done clear
  B)
   \[\text{45}{}^\circ \]  done clear
  C)
   \[\text{2}0{}^\circ \]      done clear
  D)
          \[\text{3}0{}^\circ \] done clear
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• question_answer55)
  In \[\Delta ABC\], if\[\angle \text{B}=\text{9}0{}^\circ ,\text{AB}=\text{5 cm}\] and AC =10 cm, find\[\angle A\]and\[\angle C\]
  A)
   \[~\text{9}0{}^\circ ,\text{ 45}{}^\circ \]               done clear
  B)
   \[\text{6}0{}^\circ ,\text{ 3}0{}^\circ \] done clear
  C)
   \[\text{45}{}^\circ ,\text{ }0{}^\circ \]                    done clear
  D)
   \[~\text{9}0{}^\circ ,\text{ 6}0{}^\circ \] done clear
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• question_answer56)
  lf \[\frac{\sin \theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{\sqrt{3}+1}{\sqrt{3}-1}\]find the acute angle\[\theta \].
  A)
   \[\text{9}0{}^\circ \]                                      done clear
  B)
   \[\text{45}{}^\circ \] done clear
  C)
   \[\text{3}0{}^\circ \]                      done clear
  D)
          \[\text{6}0{}^\circ \] done clear
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• question_answer57)
  If \[2(\cos \theta +\sec \theta )=5\], what is the value of\[{{\cos }^{2}}\theta +{{\sec }^{2}}\theta \]?
  A)
   \[\frac{25}{2}\]                                done clear
  B)
   \[\frac{5}{4}\]   done clear
  C)
   \[\frac{17}{4}\]                done clear
  D)
          \[\frac{4}{17}\] done clear
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• question_answer58)
  How is \[\cot \theta \] expressed in terms of\[\sin \theta \]?
  A)
   \[\frac{1}{\sqrt{1-{{\sin }^{2}}\theta }}\]                              done clear
  B)
   \[\frac{\sqrt{1-{{\sin }^{2}}\theta }}{\sin \theta }\] done clear
  C)
   \[\frac{1}{\sin \theta }\]                              done clear
  D)
   \[\frac{\sin \theta }{\sqrt{1-{{\sin }^{2}}\theta }}\] done clear
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