Question

Prove:$\left(1+{\tan }^2\theta \right){\sin }^2\theta ={\tan }^2\theta$

Answer 1

We know that $1+{\tan }^2\theta ={\sec }^2\theta$

L.H.S$={\sec }^2\theta {\sin }^2\theta$

$=\frac{1}{{\cos }^2\theta }{\sin }^2\theta$

$=\frac{{\sin }^2\theta }{{\cos }^2\theta }$

$={\tan }^2\theta =$R.H.S

Hence proved.