Question

Solve the following equations.
$tanx+cotx=2.$

Answer 1

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

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

$\Rightarrow 1=2\sin x\cos x$

$\Rightarrow \sin 2x=1$

$\Rightarrow 2x=(2n+1)\frac{\pi }{2}$

$x=\frac{(2n+1)\pi }{4}$