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JEE Main 2016 (Online) 10th April Morning Slot
Subjects
Mathematics
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Competency Based
Knowledge Based
2016
JEE Main 2016 (Online) 10th April Morning Slot
Full Paper Analysis & Solutions
Mathematics
Multiple Choice Questions
1
APPLY
MCQ_SINGLE
4 Mark(s)
2016
JEE Main 2016 (Online) 10th April Morning Slot
#1068
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)
$Q \nsubseteq P$
(C)
$P \nsubseteq Q$
(D)
$P = Q$
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AI Explanation
MEDIUM
Correct Answer:
D
Explanation
Given, for set P: $sin\theta - cos\theta = \sqrt{2}cos\theta$ $sin\theta = (\sqrt{2} + 1)cos\theta$ $cos\theta = (\sqrt{2} - 1)sin\theta$ ... (1) Given, for set Q: $sin\theta + cos\theta = \sqrt{2}sin\theta$ $cos\theta = (\sqrt{2} - 1)sin\theta$ ... (2) From (1) and (2), P = Q
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