Question

Prove That √1+sine theta/√1-sine theta +√1-sine theta/√1+sine theta = 2sec theta​

Answer 1

Answer:

Given:–

$\frac{ \sqrt{1 + sinx} }{ \sqrt{1 - sinx} } + \frac{ \sqrt{1 - sinx} }{ \sqrt{1 + sinx} } = 2secx$

Take LHS,

→ $\frac{ \sqrt{1 + sinx} }{ \sqrt{1 - sinx} } + \frac{ \sqrt{1 - sinx} }{ \sqrt{1 + sinx} }$

→ $\frac{1 + sinx + 1 - sinx}{ \sqrt{1 - {sin}^{2} x} }$

As we know that,

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

→ $\frac{2}{ \sqrt{ {cos}^{2} x} }$

→ $\frac{2}{cosx}$

→ $2secx$

So,

$\frac{ \sqrt{1 + sinx} }{ \sqrt{1 - sinx} } + \frac{ \sqrt{1 - sinx} }{ \sqrt{1 + sinx} } = 2secx$