Question

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

Answer 1

${\displaystyle ({\sin }^2\theta +\frac{1}{1+{\tan }^2\theta })}$

  = ${\displaystyle ({\sin }^2\theta +\frac{1}{{\sec }^2\theta })}$

  =${\displaystyle ({\sin }^2\theta +{\cos }^2\theta )}$

 =1