Question

Find $\theta$, if $\sin 5\theta =\cos 4\theta$; where $5\theta$ and $4\theta$ are acute angles.

Answer 1

We have given

$\sin 5\theta =\cos 4\theta$

$\Rightarrow \sin 5\theta =\sin (90-4\theta )$

$\Rightarrow 5\theta =90-4\theta$

$\Rightarrow 9\theta =90$

$\therefore \theta =10$

Hence, the value of $\theta$ is $10$