Question

Solve $\sin x=\tan x$

Answer 1

We have,

$\begin{array}{c}\sin x=\tan x\\ \sin x-\tan x=0\\ \sin x-\left(\frac{\sin x}{\cos x}\right)=0\\ \sin x.\cos x-\sin x=0\\ \sin x\left(\cos x-1\right)=0\end{array}$

Either factor should be zero.

$a.sinx=0$

Unit circle gives :

$x=0,x=\pi$, and $x=2\pi$

General solution : $x=k\pi$ where $k\in Z$

$b.cosx-1=0\Rightarrow \cos x=1$

$x=0+2k\pi =2k\pi$ where $k\in Z$