1 Answer

Jorgebg · Answer 1 · 2022-10-12T21:26:09+0000

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.

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