1.4 Sum to product/product to sum

If [math]\cos^237.5^\circ-\sin^222.5^\circ=\dfrac{\sqrt{a}+\sqrt{b}}{8}[/math] where [math]a[/math] and [math]b[/math] are integers, what is the value of [math]ab[/math]?

If [math]\sin37.5^\circ\cos22.5^\circ=\dfrac{\sqrt{a}+\sqrt{b}-\sqrt{c}}{8}[/math] where [math]a, b[/math], and [math]c[/math] are integers, what is the value of [math]a+b+c[/math]?

Evaluate [math]\displaystyle{\sum^5_{k=1}\cos\frac{2k\pi}{11}}[/math]

Let [math]\sin(x+y)=0.4[/math] and [math]\sin(x-y)=0.6[/math]. Evaluate [math]\sin2x+\sin2y[/math].