Question

Find all solutions to the equation in the interval [0, 2TT). Cos x= sin 2x (1 point)

Answer 1

You can use the formula for the double angle of the sine to write

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

To turn the equation into

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

Move everything to the left hand side to have

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

Factor $\cos(x)$ to have

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

A factor equals zero if and only if one of its factor equals zero. So, either

$\cos(x)=0$

or

$2\sin(x)-1=0 \iff 2\sin(x)=1\iff \sin(x)=\dfrac{1}{2}$

I assume that you have a table to lookup for these known values. If you have troubles solving for $x$, hit me up in the comments