Question

Evaluate:

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

• A. $\sqrt{2}\cos {20}^{\circ }$
• B. $\sqrt{2}\sin {20}^{\circ }$
• C. $\sqrt{3}\cos {20}^{\circ }$
• D. $\sqrt{3}\sin {20}^{\circ }$

Answer 1

The correct option is B $\sqrt{2}\sin {20}^{\circ }$

As we know that

$\cos B-\cos A=2\sin (\frac{A+B}{2})\sin (\frac{A-B}{2})$

$\cos {25}^{\circ }-\cos {65}^{\circ }=2\sin (\frac{{65}^{\circ }+{25}^{\circ }}{2})\sin (\frac{{65}^{\circ }-{25}^{\circ }}{2})$

$=2\sin {45}^{\circ }\sin {20}^{\circ }=\sqrt{2}\sin {20}^{\circ }$