GATE | GATE-CS-2009 | Question 25

is equivalent to
(A) 0
(B) 1
(C) ln 2
(D) 1/2 ln 2


Answer: (D)

Explanation: (1-tanx)/(1+tanx) = (cosx – sinx)/(cosx + sinx)

Let cosx + sinx = t
(-sinx + cosx)dx = dt

(1/t)dt = ln t => ln(sinx + cosx)
=> ln(sin Π/4 + cos Π/4)
=> ln(1/√2 + 1/√2)
=> 1/2 ln 2

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