Question

Solve the following equations.
$cotx+\frac{sinx}{1+cosx}=2.$

Answer 1

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

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

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

$\Rightarrow \frac{1+\cos x}{\sin x(1+\cos x)}=2$

$\Rightarrow \sin x=\frac{1}{2}\Rightarrow x=\frac{\pi }{6}$