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Question
Find the integrals of the function:
`1/(cos(x - a) cos(x - b))`
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Solution
Let `I = int 1/(cos (x - a) cos (x - b)) dx`
`= 1/(sin(a - b)) int sin [(x - b) - (x - a)]/(cos (x - a) cos (x - b)) dx`
`= 1/sin (a - b) int (sin (x - b) cos (x - a) - cos (x - b) sin (x - a))/(cos (x - a) cos (x - b))dx`
`= 1/(sin (a - b)) [int tan (x - b) dx - int tan (x - a) dx]`
`= 1/(sin (a - b)) [ - log abs (cos (x - b)) + log abs (cos (x - b))] = C`
`= 1/(sin (a - b)) log abs (cos (x - a)/cos (x - b)) + C`
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