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

The correct option is B $\frac{1}{8}$

$\frac{\left(\cos {15}^{\circ }\right)2\left(\cos 7{\frac{1}{2}}^{\circ }\sin 7{\frac{1}{2}}^{\circ }\right)}{2}=\frac{\cos {15}^{\circ }\sin {15}^{\circ }}{2}=\frac{2\cos {15}^{\circ }\sin {15}^{\circ }}{4}=\frac{\sin {30}^{\circ }}{4}=\frac{1}{8}$