Question

The value of $\cos {15}^{\circ }\cos 7{\frac{1}{2}}^{\circ }\sin 7{\frac{1}{2}}^{\circ }$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{8}$
• C. $\frac{1}{4}$
• D. $\frac{1}{16}$

Answer 1

Answer: (B)

$\frac{1}{8}$

$\cos {15}^{\circ }\cos 7{\frac{1}{2}}^{\circ }\sin 7{\frac{1}{2}}^{\circ }$

$=\frac{1}{2}\cos {15}^{\circ }\left(2\cos 7{\frac{1}{2}}^{\circ }\sin 7{\frac{1}{2}}^{\circ }\right)$

(Multiply and divide by $2$)

$=\frac{1}{2}\cos {15}^{\circ }\sin {15}^{\circ }$

$=\frac{1}{4}\left(2\sin {15}^{\circ }\cos {15}^{\circ }\right)=\frac{1}{4}\left(\sin {30}^{\circ }\right)=\frac{1}{4}\cdot \frac{1}{2}=\frac{1}{8}$

Formula used: $2\sin \theta \cos \theta =\sin 2\theta$