Consider a $$\Delta$$ABC in which $$\cos A + \cos B + \cos C = \sqrt 3 \sin {\pi \over 3}$$

What is the value of $$\cos \left( {{{A + B} \over 2}} \right)\cos \left( {{{B + C} \over 2}} \right)\cos \left( {{{C + A} \over 2}} \right)$$ ?

Given that tan$$\alpha$$ and tan$$\beta$$ are the roots of the equation x² + bx + c = 0 with b $$\ne$$ 0.

What is tan ($$\alpha$$ + $$\beta$$) equal to?

Given that tan$$\alpha$$ and tan$$\beta$$ are the roots of the equation x² + bx + c = 0 with b $$\ne$$ 0.

What is $$\sin (\alpha + \beta )sec\alpha sec\beta $$ equal to?

Consider the equation $$k\sin x + \cos 2x = 2k - 7$$

If the equation possesses solution, then what is the minimum value of k?