The value of $$\cot {\pi \over {24}}$$ is :

If 15sin⁴$$\alpha$$ + 10cos⁴$$\alpha$$ = 6, for some $$\alpha$$$$\in$$R, then the value of

27sec⁶$$\alpha$$ + 8cosec⁶$$\alpha$$ is equal to :

If for x $$\in$$ $$\left( {0,{\pi \over 2}} \right)$$, log₁₀sinx + log₁₀cosx = $$-$$1 and log₁₀(sinx + cosx) = $${1 \over 2}$$(log₁₀ n $$-$$ 1), n > 0, then the value of n is equal to :

If 0 < x, y < $$\pi$$ and cosx + cosy $$-$$ cos(x + y) = $${3 \over 2}$$, then sinx + cosy is equal to :