Question

Let $P = \\{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \\}$ and $Q = \\{\theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \\}$ be two sets. Then :

• A. $P \subset Q$ and $Q -p \neq \phi$
• B. $Q ? P$
• C. $P ? Q$
• D. $P = Q$

Answer 1

Answer: (D)

$P = Q$

Answer 2

For Let $P$
$\sin \theta=\cos \theta(\sqrt{2}+1)$
$(\sqrt{2}-1) \sin \theta=\cos \theta\,\,\,\,\,\,\,...(i)$
For Let $Q$
$\cos \theta=(\sqrt{2}-1) \sin \theta\,\,\,\,\,\,\,...(ii)$
(i) & (ii) are same $P = Q$