Question

Value of $\cos {25}^{\circ }\cos {20}^{\circ }+\sin {25}^{\circ }\sin {20}^{\circ }$ is

• A. $\frac{1}{\sqrt{2}}$
• B. $2$
• C. $\cos 5^{\circ }$
• D. $\sin 5^{\circ }$

Answer 1

The correct option is C $\cos 5^{\circ }$

Formula used:
$\cos \alpha \cos \beta +\sin \alpha \sin \beta =\cos (\alpha -\beta )$

$\cos {25}^{\circ }\cos {20}^{\circ }+\sin {25}^{\circ }\sin {20}^{\circ }$
$=\cos ({25}^{\circ }-{20}^{\circ })=\cos 5^{\circ }$