Question

All the-pairs (x, y) that satisfy the inequality `2^sqrt(sin^2x  -  2sinx  +  5), 1/(4^(sin^2y)) ≤ 1` also satisfy the equation ______.

Options

• 2|sin x| = 3sin y

• 2 sin x = sin y

• sin x = 2 sin y

• sin x = |sin y|

Answer 1

All the-pairs (x, y) that satisfy the inequality `2^sqrt(sin^2x  -  2sinx  +  5), 1/(4^(sin^2y)) ≤ 1` also satisfy the equation sin x = |sin y|.

Explanation:

Given inequality is,

`2^sqrt(sin^2x  -  2sinx  +  5) ≤ 2^(2sin^2)y`

⇒ `sqrt(sin^2x - 2sinx + 5) ≤ 2sin^2y`

⇒ `sqrt((sinx - 1)^2 + 4) ≤ 2sin^2y`

It is true if sin x = 1 and |sin y| = 1

Therefore, sin x = |sin y|