InterviewSolution
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InterviewSolution
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`int_(0)^(pi//2)(1)/((1+tanx))dx=?`A. `pi`B. `pi//2`C. `pi//3`D. `pi//4` |
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Answer» Correct Answer - D Given, `l = int_(0)^(pi//2)(dx)/(1+tan x)` `l = int_(0)^(pi//2) (cos x)/(sin x + cos x)` ….(i) `l = int_(0)^(pi//2)(cos((pi)/(2)-x))/(sin((pi)/(2)-x)+cos((pi)/(2)-x))dx` `= int_(0)^(pi//2)(sin x)/(cos x+ sin x)dx` ….(ii) On adding Eqs. (i) and (ii), we get `2 l = int_(0)^(pi//2)((sin x + cos x)/(sin x + cos x))dx` `= int_(0)^(pi//2)dx = (pi)/(2)rarr l = (pi)/(4)` |
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