Question

Solve:$\sin 5\theta =\cos 2\theta ,0^o<\theta <{180}^o$

Answer 1

$sin5\theta =cos2\theta$

also,$\Rightarrow cos({90}^{\circ }-5\theta )=cos2\theta$

so,$\Rightarrow {90}^{\circ }-5\theta =2\theta$

given $(0^{\circ }<\theta <{180}^{\circ })$

thus $({90}^{\circ }=7\theta )$

$\theta =\frac{{90}^{\circ }}{7}$

$={12.8571}^{\circ }$