If $$\cos \alpha=k \cos \beta$$ then $$\cot \left(\frac{\alpha+\beta}{2}\right)$$ is equal to

If $$\sin A+\sin B=a$$ and $$\cos A+\cos B=b$$, then $$\cos (A+B)$$ equals?

What is $${{\cos \theta } \over {1 - \tan \theta }} + {{\sin \theta } \over {1 - \cot \theta }}$$ equal to?

If x and y are acute angles, such that $$\cos x + \cos y = {3 \over 2}$$ and $$\sin x + \sin y = {3 \over 4}$$, then $$\sin (x + y)$$ equals