Question

If $\cos \theta +\sin \theta =\sqrt{2}\cos \theta$ then the value of $\frac{\cos \theta -\sin \theta }{\sin \theta }$ is

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $1$
• D. None of these

Answer 1

Answer: (A)

$\sqrt{2}$

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