Integrate : $\int \large\frac{1}{\cos x - \sin x}$$dx$

Question

$(a)\;\frac{1}{\sqrt 2} \log _e \bigg|\frac{\sec^2 (x/2)+ (\sqrt 2 +1)}{(\sqrt 2 +1) \sec ^2 (x/2)}\bigg|+c \qquad(b)\;\sec^2 (x/2)+c \qquad(c)\;\cos ^2 (x/2)+c \qquad (d)\;None$