Need help in evaluating a Definite Integral I am stuck at this definite integral
$$
\int_0^{\pi/2}  \frac{1}{1-(\sin x)(\cos y)}\, dx . 
$$
I tried multiplying and dividing by $cosx$ and then using by parts integration, but I not able to proceed further .Someone please help me out .

Hint:
Try using the Weierstrass substitution ( $\tan{\left(\frac{x}{2}\right)}=t$).
You will be left with the following integral $$\int_0^1 \frac{2}{t^2-2t\cos{y}+1} \; \mathrm{d}t=\int_0^1 \frac{2}{\left(t-\cos{y}\right)^2+\sin^2y} \; \mathrm{d}t$$
