$\int \frac{\sin \left(\mathrm{x}-\mathrm{a}\right)}{\cos \left(\mathrm{x}-\mathrm{b}\right)}\mathrm{dx}=\mathrm{Alog}\left|\sec \left(\mathrm{x}-\mathrm{b}\right)\right|+\mathrm{Bx}+\mathrm{C}$ then the value of B is

$\begin{array}{l}\frac{\sin (x-a)}{\cos (x-b)}=\frac{\sin (x-b+(b-a\left)\right)}{\cos (x-b)}=\tan (x-b)\cos (b-a)+\sin (b-a)\\ \int \frac{\sin (x-a)}{\cos (x-b)}dx=\cos (b-a)\int \tan (x-b)dx+\sin (b-a)\int dx\\ =\cos (b-\text{ a) }\log |\sec (x-b)|+\sin (b-a)x+C\end{array}$