If x = sin ⁡ 2 tan - 1 ⁡ 2 3 and y = sin ⁡ 1 2 tan - 1 ⁡ 12 5 , then

Question

If x = sin ⁡ 2 tan - 1 ⁡ 2 3 and y = sin ⁡ 1 2 tan - 1 ⁡ 12 5 , then, x = 1 - y, x 2 = 1 - 2 y, x 2 = 1 + y, y 2 = x 3

MARKS App · Accepted Answer

Let x = sin ⁡ 2 θ , where tan ⁡ θ = 2 3 ⇒ x = 2 tan ⁡ θ 1 + tan 2 ⁡ θ = 4 3 1 + 12 = 4 3 13 If α = tan - 1 ⁡ 12 5 , y = sin ⁡ α 2 = 1 2 1 - cos ⁡ α = 1 2 1 - 5 13 = 2 13 ∴ y 2 = 4 13 ⇒ y 2 = x 3

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