ABC is a triangle inscribed in a circle with centre O. Let $$\alpha$$ = $$\angle$$BAC, where 45$$^\circ$$ < $$\alpha$$ < 90$$^\circ$$. Let $$\beta$$ = $$\angle$$BOC. Which one of the following is correct?

If $${{\sin (x + y)} \over {\sin (x - y)}} = {{a + b} \over {a - b}}$$, then what is $${{\tan x} \over {\tan y}}$$ equal to?

If sin$$\alpha$$ + sin$$\beta$$ = 0 = cos$$\alpha$$ + cos$$\beta$$, where 0 < $$\beta$$ < $$\alpha$$ < 2$$\pi$$, then which one of the following is correct?

Suppose cos A is given. If only one value of $$\cos \left( {{A \over 2}} \right)$$ is possible, then A must be