If ∫ 1 + tan x sin 2 x d x = A logtan x + B tan x + C then 4 A - B =

Question

If ∫ 1 + tan x sin 2 x d x = A logtan x + B tan x + C then 4 A - B =, - 1, 2, 1, - 2

MARKS App · Accepted Answer

I = ∫ 1 + tan x sin 2 x d x = ∫ 1 sin 2 x + tan x sin 2 x d x = ∫ 1 2 sin x cos x d x + ∫ sin x 2 sin x cos x cos x d x = ∫ 1 2 sin x cos x cos 2 x d x + ∫ 1 2 sin x cos x cos 2 x d x = ∫ sec 2 x 2 tan x d x + ∫ sec 2 x 2 tan x d x = 1 2 ln tan x + tan x + C So, 4 A - B = 4 × 1 2 - 1 = 1

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