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Suppose cos 2 ⁡ y ⋅ d y d x = sin ⁡ x + y + sin ⁡ x - y ,   x ≤ π 2 and y ≤ π 2 . If y π 3 = - π 2 , then y π 2 is

Options

  1. A0
  2. Bπ 4
  3. C- π 4
  4. Dπ 2

Correct answer

A. 0

Step-by-step solution

cos 2 ⁡ y d y d x = 2 sin ⁡ x cos ⁡ y ⇒ cos ⁡ y d y = 2 sin ⁡ x d x ⇒ sin ⁡ y + 2 cos ⁡ x = c Now, y π 3 = - π 2 ⇒ c = 0 So sin ⁡ y = - 2 cos ⁡ x At x = π 2 ,   sin ⁡ y = 0 ⇒ y π 2 = 0

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