Question

Write the value of $\left(1-{\cos }^2\theta \right){\mathrm{cosec}}^2\theta$.

Answer 1

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