21. If $$\sec \theta + \frac{1}{{\cos \theta }} = 2,$$ find the value of $${\sec ^{55}}\theta + \frac{1}{{{{\sec }^{55}}\theta }} = ?$$
22. Simplify the following expression:
$$\frac{{\cos A}}{{1 - \tan A}} + \frac{{\sin A}}{{1 - \cot A}} - \sin A$$
$$\frac{{\cos A}}{{1 - \tan A}} + \frac{{\sin A}}{{1 - \cot A}} - \sin A$$
23. If sinA = $$\frac{5}{{13}}$$ and 7cotB = 24, then the value of (secAcosB)(cosecBtanA) is:
24. $$\frac{{1 + \cos \theta - {{\sin }^2}\theta }}{{\sin \theta \left( {1 + \cos \theta } \right)}} \times \frac{{\sqrt {{{\sec }^2}\theta + {\text{cose}}{{\text{c}}^2}\theta } }}{{\tan \theta + \cot \theta }},$$ 0° < θ < 90°, is equal to:
25. The value of $$\frac{{\sin {{23}^ \circ }\cos {{67}^ \circ } + \sec {{52}^ \circ }\sin {{38}^ \circ } + \cos {{23}^ \circ }\sin {{67}^ \circ } + {\text{cosec}}\,{{52}^ \circ }\cos {{38}^ \circ }}}{{{\text{cose}}{{\text{c}}^2}\,{{20}^ \circ } - {{\tan }^2}{{70}^ \circ }}}{\text{ is:}}$$
26. If $${\left\{ {\left( {\frac{{\sec \theta - 1}}{{\sec \theta + 1}}} \right)} \right\}^n} = {\text{cosec}}\,\theta - \cot \theta ,$$ then n = ?
27. If cosθ = $$\frac{{12}}{{13}},$$ then the value of $$\frac{{\sin \theta \left( {1 - \tan \theta } \right)}}{{\tan \theta \left( {1 + {\text{cosec}}\theta } \right)}}$$ is:
28. If 2cos2θ + 3sinθ = 3, where 0° < θ < 90°, then what is the value of sin22θ + cos2θ + tan22θ + cosec22θ?
29. If $$\frac{{{{\sin }^2}\theta }}{{{{\cos }^2}\theta - 3\cos \theta + 2}} = 1,\,\theta $$ lies in the first quadrant, then the value of $$\frac{{{{\tan }^2}\frac{\theta }{2} + {{\sin }^2}\frac{\theta }{2}}}{{\tan \theta + \sin \theta }}$$ is:
30. The value of the expression (cos6θ + sin6θ - 1)(tan2θ + cot2θ + 2) is:
Read More Section(Trigonometry)
Each Section contains maximum 100 MCQs question on Trigonometry. To get more questions visit other sections.