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Question

Mathematics Question on Trigonometric Functions

The value of cos 15∘ cos71∘2 sin71∘215^{\circ}\, cos 7 \frac{1^{\circ}}{2}\, sin 7 \frac{1^{\circ}}{2} is

A

12\frac{1}{2}

B

18\frac{1}{8}

C

14\frac{1}{4}

D

116\frac{1}{16}

Answer

18\frac{1}{8}

Explanation

Solution

cos 15∘ cos 71∘2 sin 7 1∘2=(2 sin 71∘2)cos 15∘2=12×14=18cos\,15^{\circ}\,cos\,7 \frac{1^{\circ}}{2}\,sin\,7\, \frac{1^{\circ}}{2}=\frac{\left(2\,sin\,7 \frac{1^{\circ}}{2}\right)cos\,15^{\circ}}{2}=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}