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

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, $ P \subset Q $ and $ P \neq \varnothing $, $ Q \not \subset P $, $ P \not \subset Q $, $ P=Q $

MARKS App · Accepted Answer

In set P, sin ⁡ θ = 2 + 1 cos ⁡ θ ⇒ tan ⁡ θ = 2 + 1 In set Q , 2 - 1 sin ⁡ θ = cos ⁡ θ ⇒ tan ⁡ θ = 1 2 - 1 = 2 + 1 ⇒ P = Q

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