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:

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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