Question

Prove that $\frac{2}{1-\sin A}\times \frac{1}{1+\sin A}=2{\sec }^{2}A$

Answer 1

L.H.S

$\frac{2}{1-\sin A}\times \frac{1}{1+\sin A}$

We know that

$a^2-b^2=(a+b)(a-b)$

Therefore,

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

$\Rightarrow \frac{2}{{\cos }^{2}A}[\because 1-{\sin }^{2}x={\cos }^{2}x]$

$\Rightarrow 2{\sec }^{2}A$

R.H.S

Hence, proved.