Question

Find out the value of 7 theta, if sin theta =cos 4 theta.

Answer 1

Concept:

$\boxed{\bf\,cos(\frac{\pi}{2}-\theta)=sin\theta}$

Given:

$sin\,\theta=cos\,4\theta$

$\implies\,cos(\frac{\pi}{2}-\theta)=cos\,4\theta$

$\implies\,\frac{\pi}{2}-\theta=4\theta$

$\implies\,\frac{\pi}{2}=4\theta+\theta$

$\implies\,\frac{\pi}{2}=5\theta$

$\implies\,5\theta=\frac{\pi}{2}$

$\implies\,\theta=\frac{\pi}{10}$

Now,

$7\,\theta=\frac{7\pi}{10}$

Answer 2

$\huge\bf{Answer:-}$

Refer the attachment.