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Please explain as well, solve the trigonometric equation

Please explain as well, solve the trigonometric equation-example-1

1 Answer

6 votes

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.

User Jorgebg
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