Question

Integration of $\left\{\cos \right(x+a\left)/\sin \right(x+b\left)\right\}\cdot dx$.

Answer 1

$\int \frac{\cos (x+a)}{\sin (x+6)}dx$

$=\int \frac{\cos 9x+b+a-b}{\sin (x+b)}dx$

$\int \frac{\cos (x+6)+(a-6)}{\sin (x+6)}dx$

$\int \frac{\cos (x+b)}{\sin (x+b)}\cos [a-b]dx-$$\int \frac{\sin (x+b)}{\sin (x+b)}sen(a-b)dx$

$=\left(\cos \right(a-b\left)\right).\cos (x+6)dx-\int sen(a-b)dx$

$=\cos (a-b)\log \left|\sin \right(x+b\left)\right|-\sin (a-b)x+c$