Question

Prove that : ${\sec }^{2}A+\text{cosec}{}^{2}A={\sec }^{2}A\times \text{cosec}{}^{2}A$.

Answer 1

L.H.S. $={\sec }^{2}A+\text{cosec}{}^{2}A$

$\Rightarrow \frac{1}{{\cos }^{2}A}+\frac{1}{{\sin }^{2}A}$

$\Rightarrow \frac{{\sin }^{2}A+{\cos }^{2}A}{{\sin }^{2}A{\cos }^{2}A}$

$\Rightarrow \frac{1}{{\sin }^{2}A{\cos }^{2}A}$

$\Rightarrow \text{cosec}{}^{2}A{\sec }^{2}A=$ R.H.S.