Question

Find all solutions and solutions in interval[0,2pi)

Answer 1

`\bf sin(2\theta)=2sin(\theta)cos(\theta)\\\\ -------------------------------\\\\ sin(2x)-√(3)cos(x)=0\implies 2sin(x)cos(x)-cos(x)√(3)=0 \\\\\\ \stackrel{\stackrel{common}{factor}}{cos(x)}[2sin(x)-√(3)]=0\\\\ -------------------------------\\\\`


`\bf cos(x)=0\implies \measuredangle x= \begin{cases} (\pi )/(2)\\\\ (3\pi )/(2) \end{cases}\\\\ -------------------------------\\\\ 2sin(x)-√(3)=0\implies 2sin(x)=√(3)\implies sin(x)=\cfrac{√(3)}{2} \\\\\\ \measuredangle x= \begin{cases} (\pi )/(3)\\\\ (2\pi )/(3) \end{cases}`