Question

(cosec²57° − tan²33°) = ?
(a) 0
(b) 1
(c) 2
(d) None of these

Answer 1

$$\begin{gathered} \text{(b) 1} \\ \text{We have:} \\ (\cos {\text{ec}}^2{57}^0-{\tan }^2{33}^0) \\ =[\cos {\text{ec}}^2({90}^0-{33}^0)-{\tan }^2{33}^0] \\ =({\sec }^2{33}^0-{\tan }^2{33}^0)[\because \cos \text{ec}({90}^0-\theta )=\sec \theta ] \\ =1[\because {\sec }^2\theta -{\tan }^2\theta =1] \end{gathered}$$