$$ \text { If } \operatorname{cosec}(90+A)+x \cos A \cot (90+A)=\sin (90+A) \text { then the value of } x \text { is } $$

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?