Question

Write the value of ${\sin }^2\theta {\cos }^2\theta \left(1+{\tan }^2\theta \right)\left(1+{\cot }^2\theta \right)$.

Answer 1

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