Question

If $\frac{\sin x}{1+\cos x}+\frac{\sin x}{1-\cos x}=4$ and $0^0\le x\le {90}^0$, then the value of $x$ is

• A. ${10}^0$
• B. ${15}^0$
• C. ${30}^0$
• D. ${45}^0$

Answer 1

The correct option is C ${30}^0$

Given expression
$\Rightarrow \sin x\left[\frac{(1-\cos x)+(1+\cos x)}{1-{\cos }^{2}x}\right]=4$
$\Rightarrow \sin x\times \frac{2}{{\sin }^{2}x}=4$ or $\sin x=\frac{1}{2}$
$\Rightarrow x={30}^0$