If 2 sin ⁡ α 1 + cos ⁡ α + sin ⁡ α = 3 4 , then the value of 1 - cos ⁡ α + sin ⁡ α 1 + sin ⁡ α is equal to

Question

If 2 sin ⁡ α 1 + cos ⁡ α + sin ⁡ α = 3 4 , then the value of 1 - cos ⁡ α + sin ⁡ α 1 + sin ⁡ α is equal to, 4 3, 3 4, 1 4, 7 4

MARKS App · Accepted Answer

Let, x = 2 sin ⁡ α 1 + cos ⁡ α + sin ⁡ α Let, y = 1 - cos ⁡ α + sin ⁡ α 1 + sin ⁡ α . Now, x y = 2 sin ⁡ α 1 + sin ⁡ α 1 + sin ⁡ α 2 - cos 2 ⁡ α ⇒ x y = 2 sin ⁡ α 1 + sin ⁡ α 1 + sin 2 ⁡ α + 2 sin ⁡ α - 1 + sin 2 ⁡ α = 1 ⇒ x = y = 3 4

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