Integrate : $\int \large\frac{1}{\sin (x-a) \cos (x-b)}$$dx$

Question

$(a)\;\frac{1}{\cos (a-b)}\bigg[\log |\sin (x-a)|+\log | \sec (x-b)|\bigg]+c \qquad (b)\;\frac{1}{\cos (a-b)}\bigg[\log |\sin (x-a)|-\log | \sec (x-b)|\bigg]+c \\ (c)\;\frac{1}{\cos (a+b)}\bigg[\log |\sin (x-a)|+\log | \sec (x-b)|\bigg]+c \qquad (d)\;\frac{1}{\sin (a-b)}\bigg[\log |\sin (x-a)|+\log | \sec (x-b)|\bigg ]+c$