integrate1

\int \frac{dx}{sin(x-a)cos(x-b)}

=\frac{1}{cos(b-a)}\int \frac{cos(b-a)dx}{sin(x-a)cos(x-b)}

=\frac{1}{cos(b-a)}\int \frac{cos((x-a)-(x-b))dx}{sin(x-a)cos(x-b)}

=\frac{1}{cos(b-a)}\int \frac{cos(x-a)cos(x-b)+sin(x-a)sin(x-b)dx}{sin(x-a)cos(x-b)}
=\frac{1}{cos(b-a)}\int (cot(x-a)+tan(x-b))dx

now u can solve ,

and this method is general

if u have sin(x-a)cos(x-b) , in deno , den multiply divide cos function ,

and if u hav only sine or only cosine function like sin(x-a)sin(x-b)\;OR\;cos(x-a)cos(x-b),

then multiply divide sin(b-a) ,