eaglesfan1717's question at Yahoo! Answers regarding a trigonometric equation

[MarkFL]

Here is the question:

Help with trig equation ?

sin x = 2 sin x cos x

Here is a link to the question:

Help with trig equation ? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

 

[MarkFL]

Hello eaglesfan1717,

We are given to solve:

\(\displaystyle \sin(x)=2\sin(x)\cos(x)\)

I would arrange the equation so that we may factor and utilize the zero-factor property:

\(\displaystyle 2\sin(x)\cos(x)-\sin(x)=0\)

\(\displaystyle \sin(x)(2\cos(x)-1)=0\)

Equating the factors in turn to zero yields the following roots:

i) \(\displaystyle \sin(x)=0\)

\(\displaystyle x=k\pi\) where \(\displaystyle k\in\mathbb{Z}\).

ii) \(\displaystyle 2\cos(x)-1=0\)

\(\displaystyle \cos(x)=\frac{1}{2}\)

\(\displaystyle x=\pm\frac{\pi}{3}+2k\pi=\frac{\pi}{3}(6k\pm1)\)

To eaglesfan1717 and any other guests viewing this topic, I invite and encourage you to post your trigonometry questions in our Trigonometry forum.

Best Regards,

Mark.