What is #f(x) = int secx- cscx dx# if #f((5pi)/4) = 0 #?

1 Answer
Leland Adriano Alejandro
Jan 18, 2016

#f(x) = ln((sec x+tan x)/(csc x-cot x))+ ln((sqrt(2) +1)/(sqrt2-1))#

Explanation:

After integration

#f(x)=ln(sec x+tan x)-ln(csc x-cot x)+C#

#f((5 pi)/4)=ln abs(sec((5 pi)/4)+tan ((5 pi)/4))-lnabs(csc ((5 pi)/4)-cot ((5 pi)/4))+C=0#

#ln abs(-sqrt2+1)-lnabs(-sqrt2-1)+C=0#

#C=ln abs(sqrt2+1)-lnabs(1-sqrt2)#

#C=ln ((sqrt2+1)/(sqrt2-1))#

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