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int(0)^( pi/2)log(tan x+cot x)dx...

int_(0)^( pi/2)log(tan x+cot x)dx

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Prove that: int_(0)^( pi/2)log|tan x+cot x|dx=pi log_(e)2

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The value of the integral int_(0)^(pi//2)log |tan x cot x |dx is

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