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. $P\subset QandQ-P\ne \varphi$
• B. $Q\subset ̸P$
• C. $P\subset ̸Q$
• D. P = Q

Answer 1

The correct option is D P = Q

$P=\{\theta :sin\theta -cos\theta =\sqrt{2}cos\theta \}sin\theta =(\sqrt{2}+1)cos\theta ,tan\theta =\sqrt{2}+1Q=\{\theta :sin\theta +cos\theta =\sqrt{2}sin\theta \}cos\theta =(\sqrt{2}-1)sin\theta ortan\theta =\sqrt{2}+1\therefore P=Q$