Question

solve for x if cos(x-30)= sin3x

Answer 1

\[ \cos(x-30^\circ )= \sin 3x \implies \sin 3x = \sin \left(\frac \pi 2 - x+ 30^\circ\right) \] \[ \implies 3x = \frac \pi 2 - x+ \frac \pi 6 \implies x = 30^\circ \]

Answer 2

For general solution,

\[ \cos(x-30^\circ )= \sin 3x \implies \cos(x-30^\circ ) = \cos (\frac \pi 2 -3x) \] \[ \implies x = 2n\pi + \frac \pi 6 \pm \left(\frac \pi 2 -3x \right) \cdots \]