Question

Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.

Answer 1

Let `"I" = int  cos("x + a")/sin("x +b")"dx".` Then

`"I" = cos("x"+"b"+"a" -"b")/sin("x+b")"dx"`

`"I"  = int  cos{("x+b")+ ("a"- "b")}/sin("x+b")"dx"`

`"I"  = int  (cos("x+b").cos("a"-"b")-sin("x+b").sin("a"-"b"))/sin("x+b")"dx"`

`"I" = int [cos("a"-"b") . cot ("x+b") - sin("a"-"b")]"dx"`

`"I" = cos("a"-"b") . log |sin("x + b")| - "x".sin("a" - "b")`