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

Question

(A) \(\frac{1}{2}\)
(B) \(\frac{1}{8}\)
(C) \(\frac{1}{4}\)
(D) \(\frac{1}{16}\)

Answer 1

Ans: (B)
Hint : \(\cos 15^{\circ} \cos 7 \frac{1^{0}}{2} \sin 7 \frac{1^{0}}{2}=\frac{\left(2 \sin 7 \frac{1^{0}}{2} \cos 7 \frac{1^{0}}{2}\right) \cos 15^{\circ}}{2}=\frac{1}{2} \times \frac{1}{4}=\frac{1}{8}\)