Question

If $\cos 2\theta =\sin 4\theta$, where $2\theta$ and $4\theta$ are acute angles, find the value of $\theta$.

Answer 1

Given,

$2\theta$ and $4\theta$ are acute and $\cos 2\theta =\sin 4\theta$

We have, $\cos \theta =\sin ({90}^{\circ }-\theta )$

$\cos 2\theta =\sin ({90}^{\circ }-2\theta )$

$\therefore \sin ({90}^{\circ }-2\theta )=\sin 4\theta$

${90}^{\circ }-2\theta =4\theta$

${90}^{\circ }=2\theta +4\theta$

$6\theta ={90}^{\circ }$

$\theta ={15}^{\circ }$