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If the integral ∫ 5  tan  x tan  x - 2 dx = x + a  log sin  x - 2  cos  x + k , then the value of a is

Options

  1. A1
  2. B2
  3. C- 1
  4. D- 2

Correct answer

B. 2

Step-by-step solution

∫ 5 tan x tan x - 2 dx = x + a ln sin x - 2 cos x + k Differentiating both sides, we get 5 tan x tan x - 2 = 1 + a cos x + 2 sin x sin x - 2 cos x ⇒ 5 sin x sin x - 2 cos x = sin x 1 + 2 a + cos x a - 2 sin x - 2 cos x ⇒ a = 2

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