Question

$(1+{\tan }^2\theta )(1+{\cot }^2\theta )=\frac{1}{({\sin }^2\theta -{\sin }^4\theta )}$.

Answer 1

$\left(1+{\tan }^2\theta \right)\left(1+{\cot }^2\theta \right)=\frac{1}{{\sin }^2\theta -{\sin }^4\theta }\Rightarrow {\sec }^2\theta .\cos e{c}^2\theta \Rightarrow \frac{1}{{\cos }^2\theta }+\frac{1}{{\sin }^2\theta }\Rightarrow \frac{{\sin }^2\theta +{\cos }^2\theta }{{\sin }^2\theta .{\cos }^2\theta }\Rightarrow \frac{1}{{\sin }^2\theta \left(1-{\sin }^2\theta \right)}\Rightarrow \frac{1}{\left({\sin }^2\theta -{\sin }^4\theta \right)}$