Question

If $\sin 2\theta =\cos (\theta +6^{\circ })$ and $\theta +6^{\circ }$ are acute angles,find the value of $\theta$

Answer 1

We have $\sin 2\theta =\cos (\theta +6^{\circ })$

and $\cos ({90}^{\circ }-2\theta )=\cos (\theta +6^{\circ })$

$\Rightarrow {90}^{\circ }-2\theta =\theta +6^{\circ }$

$\Rightarrow 3\theta ={90}^{\circ }-6^{\circ }={84}^{\circ }$

$\therefore \theta =\frac{{84}^{\circ }}{3}={28}^{\circ }$