JEE Mains · Maths · STD 11 - Trigonometrical equations
Let \(P = \left\{ {\theta :\sin \,\theta - \cos \,\theta = \sqrt 2 \,\cos \,\theta } \right\}\) and \(Q = \left\{ {\theta :\sin \,\theta + \cos \,\theta = \sqrt {2\,} \sin \,\theta } \right\}\) be two sets. Then
- A \(P \subset Q\) and \(Q - P \ne \phi \)
- B \(Q \not\subset P\)
- C \(P = Q\)
- D \(P \not\subset Q\)
Answer & Solution
Correct Answer
(C) \(P = Q\)
Step-by-step Solution
Detailed explanation
\(\sin \,\theta \, - \,\cos \,\theta \,\, = \,\,\sqrt 2 \,\cos \,\theta \) \( \Rightarrow \,\sin \,\theta \, = \,\cos \,\theta \,\, + \,\,\sqrt 2 \,\cos \,\theta \)…
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