1 Answer

Answered by
9 years ago
The actual question should be [0,/4] log ( 1 + tan x ) dx.
say, I= [0,/4] log ( 1 + tan x ) dx.(1)
now , [a,0]f(x)dx= [a,0]f(a-x)dx
therefore,
I = [0,/4]log[1+tan(/4-x)]dx
= [0,/4]log{1+(1-tanx)/(1+tanx)}dx
= [0,/4]{ log2-log(1+tanx)}dx.(2)
/4
now, (1)+(2)= 2I= [0,/4](log2)dx= (log2
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