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AP EAMCET20224 Jul 2022Evening ShiftMathematicsIndefinite IntegrationActual

∫ 1 + tan x tan x + a tan x tan x + a d x =

Options

  1. Atan a log sec x + a + logsec x + C
  2. Bcot a log sin x - log sin x + a + C
  3. Ctan a log cos x sin x + a + C
  4. Dcot a log sin x + a cos x + a + C

Correct answer

B. cot a log sin x - log sin x + a + C

Step-by-step solution

I = ∫ 1 + tan x tan x + a tan x tan x + a d x We know tan a = tan x + a - x = tan x + a - tan x 1 + tan x tan x + a So, I = cot a ∫ tan x + a - tan x tan x + a tan x d x = cot a ∫ 1 tan x - 1 tan x + a d x = cot a log sin x - log sin x + a + C

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