Solving an Equation with Trigonometric Functions

[donald]

Hello, I am trying to solve the following equation:

\(\displaystyle -2*sin(2x) + 2 \sqrt{3} * cos(2x) = 0\)

The only thing I can think of is trying the double angle identity for cos, which gives me:

\(\displaystyle -2*sin(2x) + 2 \sqrt{3} - 4 \sqrt{3} * sin^2(x) = 0\)

That leaves me with a sin(2x) that I can't get rid of (preventing me from using the quadratic equation).

Surely there is some easier way to solve this?

Thanks!

 

[galactus]

You could rewrite it as:

\(\displaystyle 2\sqrt{3}cos(2x)-2sin(2x)=4cos\left(2x+\frac{\pi}{6}\right)\)

Or, assuming \(\displaystyle cos(2x)\neq 0\)

\(\displaystyle 2\sqrt{3}cos(2x)=2sin(2x)\)

\(\displaystyle 2\sqrt{3}=2tan(2x)\)

Don't forget to tack a \(\displaystyle \frac{\pi C}{2}\) onto your result.