If ∫ cos 4 x + 1 cot x - tan x = k cos 4 x + c , then " k " is equal to

Question

If ∫ cos 4 x + 1 cot x - tan x = k cos 4 x + c , then " k " is equal to, - 1 2, - 1 8, - 1 3, - 1 5

MARKS App · Accepted Answer

∫ cos 4 x + 1 cot x - tan x = ∫ cos 4 x + 1 cos 2 x - sin 2 x cos x sin x Use: cos 2 x = 2 cos 2 x - 1 = 1 - 2 sin 2 x = ∫ 2 cos 2 2 x cos 2 x × sin x cos x d x = 1 2 ∫ 2 cos 2 x sin 2 x d x = 1 2 ∫ sin 4 x d x = 1 2 × - cos 4 x 4 + c = - 1 8 cos 4 x + c ⇒ k = - 1 8

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