Question

Integrate the following : (I) 1/cos(x-alpha) cos(x-Beta) dx

Answer 1

multiply and divide by sin(beta-alpha).
sin(beta-alpha)= sin{(x-alpha)-(x-beta)}.
in the next step, expand this above equation.
in the final steps, you will have to integrate in the form of tan function.
ask if you still have doubts :)