Question

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

• A. $\sqrt{2}\cos \theta$
• B. $\sqrt{2}\sin \theta$
• C. $\sqrt{2}(\cos \theta +\sin \theta )$
• D. none of these

Answer 1

Answer: (B)

$\sqrt{2}\sin \theta$

Given $\sin \theta +\cos \theta =\sqrt{2}\cos \theta$

$⟹\sin \theta =(\sqrt{2}-1)\cos \theta$

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

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