Question

Show that : ${\sec }^2\theta \times {\csc }^2\theta ={\sec }^2\theta +{\csc }^2\theta$

Answer 1

$LHS={\text{sec}}^2\theta \times {\text{cosec}}^2\theta =\frac{1}{{\sin }^2\theta {\cos }^2\theta }=\frac{{\sin }^2\theta +{\cos }^2\theta }{{\sin }^2\theta {\cos }^2\theta }={\text{sec}}^2\theta +{\text{cosec}}^2\theta =RHS$