Question

Evaluate (Sec^2theta -1)(1 - cosec^2theta)

Answer 1

$$\begin{gathered} \left({\sec }^2\mathrm{\theta }-1\right)\left(1-{\mathrm{cosec}}^2\mathrm{\theta }\right) \\ =-\left({\sec }^2\mathrm{\theta }-1\right)\left({\mathrm{cosec}}^2\mathrm{\theta }-1\right) \\ =-{\tan }^2\mathrm{\theta }\times {\cot }^2\mathrm{\theta } \\ =-{\tan }^2\mathrm{\theta }\times \frac{1}{{\tan }^2\mathrm{\theta }} \\ =-1 \end{gathered}$$