Question

Answer 1

\(sinx\cdot cosx+\sqrt{3}\cdot sinx2x=0\)

\(\Leftrightarrow\dfrac{1}{2}\cdot sin2x+\sqrt{3}sin2x=0\)

\(\Leftrightarrow sinx2x=0\)

\(\Leftrightarrow2x=k\pi\left(k\in Z\right)\)

\(\Leftrightarrow x=\dfrac{k\cdot\pi}{2}\)

Answer 2

\(\Leftrightarrow\dfrac{1}{2}sin2x+\sqrt{3}sin2x=0\)

\(\Leftrightarrow\left(2\sqrt{3}+1\right)sin2x=0\)

\(\Leftrightarrow sin2x=0\)

\(\Leftrightarrow2x=k\pi\)

\(\Leftrightarrow x=\dfrac{k\pi}{2}\)