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The length of the longest interval in which the function y = sin ⁡ 2 x - 2 sin ⁡ x increases for x ∈ 0 , π is

Options

  1. Aπ 2
  2. Bπ 3
  3. C2 π 3
  4. Dπ 6

Correct answer

B. π 3

Step-by-step solution

d y d x = 2 cos ⁡ 2 x - 2 c o s x = 2 2 c o s 2 x - cos ⁡ x - 1 = 2 2 cos ⁡ x + 1 cos ⁡ x - 1 ∴ y increases in 2 π 3 , π

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