Question

Please explain as well, solve the trigonometric equation

Answer 1

Given:

The trigonometric equation is:

$\tan x\sin x=\tan x\cos x$

To find:

The solutions for the given equation over $0^\circ$.

Solution:

We have,

$\tan x\sin x=\tan x\cos x$

It can be written as

$\tan x\sin x-\tan x\cos x=0$

$\tan x(\sin x-\cos x)=0$

$\tan x=0$ and $(\sin x-\cos x)=0$

The solutions over $0^\circ$ are:

$x=90^\circ,180^\circ$ and $\sin x=\cos x$

$x=90^\circ,180^\circ$ and $x=45^\circ, 225^\circ$

Therefore, the correct option is D.