Question

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

Answer 1

When $\cot x$ is positive

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

$\csc x=0$

Not possible

When $\cot x$ is negative

$-\cot x=\cot x+\frac{1}{\sin x}$

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

$\Rightarrow \cos x=\frac{-1}{2}$

$\cos x=\pi +\frac{\pi }{3}\Rightarrow \frac{1}{3}\pi$