Question

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

Answer 1

`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))`