Question

What are solutions to the equation sinx cosx = square root 3 over4

Answer 1

$\sin(x)\cos(x)=\dfrac{\sqrt{3}}{4}\\\\2\sin(x)\cos(x)=\dfrac{\sqrt{3}}{2}\\\\\sin(2x)=\dfrac{\sqrt{3}}{2}\\\\2x=\arcsin\left( \dfrac{\sqrt{3}}{2} \right)\\\\2x=\left\{ \dfrac{\pi}{3},\dfrac{2\pi}{3}\right\}+2n\pi\\\\\boxed{x=\left\{ \dfrac{\pi}{6},\dfrac{\pi}{3}\right\}+n\pi}$