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

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

Consider the following statements

1. If ABC is an equilateral triangle, then $$3\tan (A + B)\tan C = 1$$.

2. If ABC is a triangle in which A = 78$$^\circ$$, B = 66$$^\circ$$, then $$\tan \left( {{A \over 2} + C} \right) < \tan A$$

3. If ABC is any triangle, then $$\tan \left( {{{A + B} \over 2}} \right)\sin \left( {{C \over 2}} \right) < \cos \left( {{C \over 2}} \right)$$

Which of the above statements is/are correct?

If $$A = (\cos 12^\circ - \cos 36^\circ )(\sin 96^\circ + \sin 24^\circ )$$ and $$B = (\sin 60^\circ - \sin 12^\circ )(\cos 48^\circ - \cos 72^\circ )$$, then what is $${A \over B}$$ equal to?

The value of $$\tan 9^\circ - \tan 27^\circ - \tan 63^\circ + \tan 81^\circ $$ is equal to