Question:
All the pairs (x, y) that satisfy the inequality
$2 \sqrt{\sin ^{2} x-2 \sin x+5} \cdot \frac{1}{4^{\sin ^{2} y}} \leq 1$ also satisfy the eauation
Correct Option: 1
Solution:
$2^{\sqrt{\sin ^{2} x-2 \sin x+5}} \cdot 4^{-\sin ^{2} y} \leq 1$
$\Rightarrow 2^{\sqrt{(\sin x-1)^{2}+4}} \leq 2^{2 \sin ^{2} y}$
$\Rightarrow \sqrt{(\sin x-1)^{2}+4} \leq 2 \sin ^{2} y$
$\Rightarrow \sin x=1$ and $|\sin y|=1$
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