Question

Find the values of $\theta$,( in degrees) if $\sin (\theta +24)=\cos \theta$, where $(\theta +24{)}^0$ is an acute angle .

Answer 1

$\sin (\theta +{24}^{\circ })=\cos \theta$

$\Rightarrow \sin (\theta +{24}^{\circ })=\sin ({90}^{\circ }-\theta )$ since $\sin ({90}^{\circ }-\theta )=\cos \theta$

$\Rightarrow \theta +{24}^{\circ }={90}^{\circ }-\theta$

$\Rightarrow 2\theta ={90}^{\circ }-{24}^{\circ }={66}^{\circ }$

$\therefore \theta =\frac{{66}^{\circ }}{2}={33}^{\circ }$