Question

Solve $(se{c}^2\theta -1)(1-cose{c}^2\theta )=-1$

Answer 1

$({\sec }^2\theta -1)(1-{\csc }^2\theta )=\left({\tan }^2\theta \right)(-{\cot }^2\theta )=-1$

( as ${\sec }^2\theta -{\tan }^2\theta =1\Rightarrow {\sec }^{\theta }-1={\tan }^2\theta$)

(as ${\csc }^2\theta -{\cot }^2\theta =1\Rightarrow 1-{\csc }^2\theta =-{\cot }^2\theta$)

( as ${\cot }^2\theta =\frac{1}{{\tan }^2\theta }$)