Question

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

Answer 1

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