All the pairs ( x , y ) , that satisfy the inequality 2 s i n 2 x - 2 s i n x + 5 · 1 4 s i n 2 y ≤ 1 also satisfy the equation:

Question

All the pairs ( x , y ) , that satisfy the inequality 2 s i n 2 x - 2 s i n x + 5 · 1 4 s i n 2 y ≤ 1 also satisfy the equation:, 2 sin x = sin y, sin x = 2 sin y, sin x = sin y, 2 sin x = 3 sin y

MARKS App · Accepted Answer

Given inequality is 2 sin 2 ⁡ x - 2 sin ⁡ x + 5 ≤ 4 sin 2 ⁡ y ⇒ sin 2 ⁡ x - 2 sin ⁡ x + 1 + 4 ≤ 2 sin 2 ⁡ y ⇒ sin ⁡ x - 1 2 + 4 ≤ 2 sin 2 ⁡ y ∵ 2 sin 2 ⁡ y ∈ 0 , 2 & sin ⁡ x - 1 2 + 4 ∈ 2 , 2 2 ∵ Only equality holds ⇒ sin ⁡ x - 1 2 + 4 = 2 sin 2 ⁡ y = 2 ⇒ sin ⁡ x - 1 2 + 4 = 4 sin 4 ⁡ y = 4 ⇒ sin 2 ⁡ y = 1 ⇒ sin ⁡ y = 1 & sin ⁡ x - 1 2 = 0 ⇒ sin ⁡ x = 1 ∴ sin ⁡ y = sin ⁡ x

Search any question & find its solution

Looking for more such questions to practice?