Question

All the pairs (x, y) that satisfy the inequality $2 \sqrt{\sin^2 x - 2 \sin x +5} . \frac{1}{4^{\sin^2 y}} \le 1 $ also satisfy the eauation.

• A. sin x = |siny|
• B. sin x = 2 sin y
• C. 2|sinx| = 3siny
• D. 2sin x = siny

Answer 1

Answer: (A)

$2\sqrt{\sin^{2}x-2\sin x+5} . 4 ^{-\sin^2y} \le 1$
$ \Rightarrow 2^{\sqrt{\left(\sin x-1\right)^2+4}} \le 2^{2\sin^2y} $
$ \Rightarrow \sqrt{\left(\sin x-1\right)^{2}+4} \le2 \sin^{2}y $
$ \Rightarrow \sin x=1$ and $ |\sin y| =1$