Find all values of X in the interval [0,2pi]
sin 2x =cos x
3
Assuming that it is $\displaystyle sin(2x)= \sqrt{3}cos(x)$, use a trig identity: $\displaystyle sin(2x)= 2sin(x)cos(x)= \sqrt{3}cos(x)$ one solution is cos(x)= 0 which gives $\displaystyle x= \pi/2$. If cos(x) is NOT 0, we can divide both sides to get $\displaystyle 2sin(x)= \sqrt{3}$ so that $\displaystyle sin(x)= \frac{\sqrt{3}}{2}$. Can you solve that?