Question

Solve in radians for 6sin2(x)=6cos(x)

Answer 1

An important trigonometric function is sin(2x):

`\sin (2x)=2\cdot\sin x\cdot\cos x`

Let's use it to solve the given equation.

`\begin{gathered} 6\cdot\sin (2x)=6\cos x \\ 6\cdot2\cdot\sin x\cdot\cos x=6\cos x \\ \sin x=(6\cdot\cos x)/(2\cdot6\cdot\cos x) \\ \sin x=(1)/(2) \\ x=\sin ^(-1)((1)/(2)) \\ x=(\pi)/(6) \end{gathered}`