Question

Cos theta + sin theta equal to root 2 cos theta then show that cos theta minus sin theta equals to root 2 sin theta

Answer 1

See the attachment for detail solution
Hope it will help you

Answer 2

Answer and explanation:

Given : $\cos \theta +\sin\theta=\sqrt2\cos\theta$

To show : $\cos\theta-\sin\theta=\sqrt{2}\sin\theta$

Solution :

We have given,

$\cos \theta +\sin\theta=\sqrt2\cos\theta$

$\sin\theta=\sqrt2\cos\theta-\cos \theta$

$\sin\theta=\cos\theta(\sqrt2-1)$

$\cos\theta=\frac{\sin\theta}{\sqrt2-1}$

$\cos\theta=\frac{\sin\theta}{\sqrt2-1}\times \frac{\sqrt2+1}{\sqrt+1}$

$\cos\theta=\frac{(\sqrt2+1)\sin\theta}{(\sqrt2)^2-1^2}$

$\cos\theta=\frac{(\sqrt2+1)\sin\theta}{2-1}$

$\cos\theta=(\sqrt2+1)\sin\theta$

$\cos\theta=\sqrt2\sin\theta+\sin\theta$

$\cos\theta-\sin\theta=\sqrt2\sin\theta$

We get the required result.