If $$\theta = {\pi \over 8}$$, then what is the value of $${(2\cos \theta + 1)^{10}}{(2\cos 2\theta - 1)^{10}}{(2\cos \theta - 1)^{10}}{(2\cos 4\theta - 1)^{10}}$$ ?

If cos $$\alpha$$ and cos $$\beta$$ (0 < $$\alpha$$ < $$\beta$$ < $$\pi$$) are the roots of the quadratic equation 4x² $$-$$ 3 = 0, then what is the value of sec $$\alpha$$ $$\times$$ sec $$\beta$$ ?

If $$A = {\sin ^2}\theta + {\cos ^4}\theta $$, then for all real $$\theta$$, which one of the following is correct?

What is $${{\sin 5x - \sin 3x} \over {\cos 5x + \cos 3x}}$$ equal to?