## Trigonometry Questions MCQs ### Total Questions : 205

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Question 1. The value of the expression:
sin21° + sin211° + sin221° + sin231° + sin241° + sin245° + sin249° + sin259° + sin269° + sin279° + sin289° is?
Question 2. If cos20° = m and cos70° =n, then the value of m2 + n2 is?
1.    $$\frac{1}{2}$$
2.    1
3.    $$\frac{3}{2}$$
4.    $$\frac{1}{{\sqrt 2 }}$$
Question 3. If $${\text{sin}}\left( {{{90}^ \circ } - \theta } \right)$$   + $${\text{cos}}\theta$$  = $$\sqrt 2 {\text{cos}}\left( {{{90}^ \circ } - \theta } \right){\text{,}}$$    then the value of $${\text{cosec}}\theta$$   is?
1.    $$\frac{1}{{\sqrt 3 }}$$
2.    $$\frac{2}{3}$$
3.    $$\sqrt {\frac{3}{2}}$$
4.    $$\frac{1}{{\sqrt 2 }}$$
Question 4. If $${\text{sin A}} - \cos {\text{A}}$$   = $$\frac{{\sqrt 3 - 1}}{2}{\text{,}}$$   then the value of $${\text{sin A}}.{\text{cosA}}$$   is?
1.    $$\frac{1}{{\sqrt 3 }}$$
2.    $$\frac{{\sqrt 3 }}{2}$$
3.    $$\frac{1}{4}$$
4.    $$\frac{{\sqrt 3 }}{4}$$
Question 5. If $$\frac{{{{\sec }^2}{{70}^ \circ } - {\text{co}}{{\text{t}}^2}{{20}^ \circ }}}{{2\left( {{\text{cose}}{{\text{c}}^2}{{59}^ \circ } - {{\tan }^2}{{31}^ \circ }} \right)}}$$     = $$\frac{2}{m}{\text{,}}$$  then m is equal to?
1.    2
2.    3
3.    4
4.    1
Question 6. $$\frac{{{\text{tan}}\theta + \cot \theta }}{{{\text{tan}}\theta - \cot \theta }} = 2,$$   $$\left( {0 \leqslant \theta \leqslant {{90}^ \circ }} \right),$$   then the value of $$\sin \theta$$  is?
1.    $$\frac{2}{{\sqrt 3 }}$$
2.    $$\frac{{\sqrt 3 }}{2}$$
3.    $$\frac{1}{2}$$
4.    1
Question 7. $$\frac{{\sin \theta + \cos \theta }}{{{\text{sin}}\theta - \cos \theta }} = 3,$$    then the value of $${\sin ^4}\theta - {\text{co}}{{\text{s}}^4}\theta$$    is?
1.    $$\frac{1}{5}$$
2.    $$\frac{3}{5}$$
3.    $$\frac{2}{5}$$
4.    $$\frac{4}{5}$$
Question 8. If $${\text{tan}}\left( {\frac{\pi }{2} - \frac{\theta }{2}} \right) = \sqrt 3$$     the value of cosθ is?
Question 9. If A = tan11°. tan29°, B = 2cot61°. cot79° then -
1.    A = 2B
2.    A = -2B
3.    2A = B
4.    2A = -B
Question 10. If tan15° = 2 - $$\sqrt 3 ,$$  then the value of tan15° cot75° + tan75° cot15° is?
1.    14
2.    12
3.    10
4.    8
Question 11. If α + β = 90°, then the value of (1 - sin2α)(1 - cos2α) × (1 + cot2β)(1 + tan2β) is?
1.    1
2.    -1
3.    0
4.    2
Question 12. If $${\text{tan }}{9^ \circ } = \frac{p}{q}{\text{,}}$$   then the value of $$\frac{{{\text{se}}{{\text{c}}^2}{\text{8}}{{\text{1}}^ \circ }}}{{1 + {{\cot }^2}{{81}^ \circ }}}$$   is?
1.    $$\frac{p}{q}$$
2.    1
3.    $$\frac{{{p^2}}}{{{q^2}}}$$
4.    $$\frac{{{q^2}}}{{{p^2}}}$$
Question 13. If 7sin2θ + 3cos2θ = 4, (0° ≤ θ ≤ 90°), then the value of θ is?
1.    $$\frac{\pi }{2}$$
2.    $$\frac{\pi }{3}$$
3.    $$\frac{\pi }{6}$$
4.    $$\frac{\pi }{4}$$
Question 14. The value of following is, cos24° + cos55° + cos125° + cos204° + cos300° ?
1.    $$- \frac{1}{2}$$
2.    $$\frac{1}{2}$$
3.    2
4.    1
Question 15. If tan(2θ + 45°) = cot3θ, where (2θ + 45°) and 3θ are acute angles, then the value of θ is?
1.    5°
2.    9°
3.    12°
4.    15°
Question 16. In sin(A - B) = $$\frac{1}{2}$$ and cos(A + B) =$$\frac{1}{2}$$ where A > B > 0 and A + B is an acute angle, then the value of B is?
1.    $$\frac{\pi }{6}$$
2.    $$\frac{\pi }{{12}}$$
3.    $$\frac{\pi }{4}$$
4.    $$\frac{\pi }{2}$$
Question 17. If 2(cos2θ - sin2θ) = 1, (θ is positive acute angle), then cotθ is equal to?
1.    $$- \sqrt 3$$
2.    $$\frac{1}{{\sqrt 3 }}$$
3.    1
4.    $$\sqrt 3$$
Question 18. Sin2θ - 3sinθ +2 = 0, will be true if ?
1.    0 ≤ θ ≤ 90°
2.    0 < θ < 90°
3.    θ = 0°
4.    θ = 90°
Question 19. If $$\sin \alpha + \cos \beta = 2;$$   $$\left( {{0^ \circ } \leqslant \beta < \alpha \leqslant {{90}^ \circ }} \right){\text{,}}$$     then $${\text{sin}}\,{\left( {\frac{{2\alpha + \beta }}{3}} \right)^ \circ }$$   is?
1.    $${\text{sin }}\frac{\alpha }{2}$$
2.    $$\cos \frac{\alpha }{3}$$
3.    $${\text{sin }}\frac{\alpha }{3}$$
4.    $$\cos \frac{{2\alpha }}{3}$$
Question 20. If $$2\sin \left( {\frac{{\pi x}}{2}} \right) = {x^2} + \frac{1}{{{x^2}}}{\text{,}}$$     then the value of $$\left( {x - \frac{1}{x}} \right)$$   is?