Question

$\sin 5\theta =\cos 2\theta ,0^o<\theta <{120}^o$.

Answer 1

$\begin{array}{c}\sin 5\theta =\cos 2\theta \\ \sin 5\theta =\sin \left(\frac{\pi }{2}-2\theta \right)\\ 5\theta =\frac{\pi }{2}-2\theta \\ 7\theta =\frac{\pi }{2}\\ \theta =\frac{\pi }{14}itsatisfiestheconditionThen,0^{\circ }<\frac{\pi }{14}<{120}^{\circ }\end{array}$