Question

Prove that ${\cos }^2\theta =\frac{1}{1+{\tan }^2\theta }$

Answer 1

Method-1:

LHS $={\cos }^2\theta =\frac{1}{{\sec }^2\theta }=\frac{1}{1+{\tan }^2\theta }=$ RHS (As ${\sec }^2\theta =1+{\tan }^2\theta$)

Method-2
RHS $=\frac{1}{1+{\tan }^2\theta }=\frac{1}{{\sec }^2\theta }={\cos }^2\theta =$ LHS