Question

If $\cos \theta +\sin \theta =\sqrt{2}\cos \theta$ then $\cos \theta -\sin \theta$ is equal to

• A. $\sqrt{2}\cos \theta$
• B. $\sqrt{2}\sin \theta$
• C. $2\cos \theta$
• D. $2\sin \theta$

Answer 1

The correct option is B $\sqrt{2}\sin \theta$

$\cos \theta +\sin \theta =\sqrt{2}\cos \theta$
$\Rightarrow \sin \theta =\cos \theta (\sqrt{2}-1)$
$\Rightarrow (\sqrt{2}+1)\sin \theta =\cos \theta (\sqrt{2}-1)(\sqrt{2}+1)=\cos \theta$
$\therefore \cos \theta -\sin \theta =\sqrt{2}\sin \theta$