What is the definite integral of log (tan x) with range from 90 to 0

Substituting x with π/2 - x gives the equivalent integral,

So if we let J denote the value of the integral, we have

Condensing the logarithms, we have

log(tan(x)) + log(cot(x)) = log(tan(x) cot(x)) = log(1) = 0

since cot(x) = 1/tan(x), which means

and so the original integral has a value of J = 0.

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step-by-step explanation:

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