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Question: Answered & Verified by Expert
Let $A=\left\{\theta \in R \mid \cos ^{2}(\sin \theta)+\sin ^{2}(\cos \theta)=1\right\}$ and $B=\{\theta \in R \mid \cos (\sin \theta) \sin (\cos \theta)=0\} .$ Then $A \cap B$
MathematicsSets and RelationsKVPYKVPY 2011 (SB/SX)
Options:
  • A is the empty set
  • B has exactly one element
  • C has more than one but finitely many elements.
  • D has infinitely many elements
Solution:
2485 Upvotes Verified Answer
The correct answer is: is the empty set
for $A \cap B$
$\cos (\sin \theta)=1$ or $-1 \& \sin (\cos \theta)=0$
which is not possible
or $\cos (\sin \theta)=0 \& \sin (\cos \theta)=1$ or $-1$
also not possible
so $A \cap B$ is an empty set

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