Question

Solve $\cos {25}^{\circ }-\cos {65}^{\circ }$

Answer 1

$cos{25}^{\circ }-cos{65}^{\circ }=2sin\left(\frac{{25}^{\circ }+{65}^{\circ }}{2}\right)sin\left(\frac{{65}^{\circ }-{25}^{\circ }}{2}\right)2sin{45}^{\circ }sin{20}^{\circ }=2\cdot \left(\frac{1}{\sqrt{2}}\right)\cdot sin{20}^{\circ }=\sqrt{2}sin{20}^{\circ }$