Question

The value of $\frac{{\tan }^2\mathrm{\theta }-{\sec }^2\mathrm{\theta }}{{\cot }^2\mathrm{\theta }-{\mathrm{cosec}}^2\mathrm{\theta }}$ is
(a) –1

(b) $\frac{1}{2}$

(c) $\frac{-1}{2}$

(d) 1

Answer 1

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

Hence, the correct answer is option (d).