Question

Prove that
${\sec }^{2}x+{\csc }^{2}x={\sec }^{2}x.{\csc }^{2}x$

Answer 1

L.H.S

${\sec }^{2}x+{\csc }^{2}x$

$=\frac{1}{{\cos }^{2}x}+\frac{1}{{\sin }^{2}x}$

$=\frac{{\sin }^{2}x+{\cos }^{2}x}{si{n}^{2}x{\cos }^{2}x}$

We know that

${\sin }^{2}x+{\cos }^{2}x=1$

Therefore,

$=\frac{1}{si{n}^{2}x{\cos }^{2}x}$

$={\sec }^{2}x{\csc }^{2}x$

Hence, proved.