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  4. Let P = θ: sin θ- cos θ=√2 cos θ and Q = θ: sin θ+ cos θ=√2 sin θ be two sets. Then

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Q. 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

JEE AdvancedJEE Advanced 2011

Solution:

In set $P , \sin \theta=(\sqrt{2}+1) \cos \theta$
$\Rightarrow \tan \theta=\sqrt{2}+1$
In set $Q,(\sqrt{2}-1) \sin \theta=\cos \theta$
$\Rightarrow \tan \theta=\frac{1}{\sqrt{2}-1}=\sqrt{2}+1$
$\Rightarrow P=Q$