Question

Write the value of $\left({\cot }^2\theta -\frac{1}{{\sin }^2\theta }\right)$.

Answer 1

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