Question:
If $\cos 2 \theta=\sin 4 \theta$, where $2 \theta$ and $4 \theta$ are acute angles, find the value of $\theta$.
Solution:
We have: $\cos 2 \theta=\sin 4 \theta$
Given in question $2 \theta$ and $4 \theta$ are acute angles. We have to find $\theta$
Now we have
$\cos 2 \theta=\sin 4 \theta$
$\Rightarrow \sin \left(90^{\circ}-2 \theta\right)=\sin 4 \theta$
$\Rightarrow 90^{\circ}-2 \theta=4 \theta$
$\Rightarrow 6 \theta=90^{\circ}$
Therefore $\theta=15^{\circ}$