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Question:

If ∫₀^π/₂ cot x / (cot x + cosec x) dx = m(π + n), then mn is equal to?

1

-1

-1/2

1/2

Solution:

Correct option is A. -1;
∫₀^π/₂ cot x dx/(cot x + cosec x) = ∫₀^π/₂ cos x dx/(cos x + 1) = ∫₀^π/₂ (1 - 1/2 sec²x/2) dx
[x - tan x/2]₀^π/₂ => 1/2[π - 2] => m = 1/2, n = -2;
mn = -1.