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<x\leq 360^\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<x\leq 360^\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.