Question

The value of $\cos {20}^{\circ }.\cos {40}^{\circ }.\cos {60}^{\circ }.\cos {80}^{\circ }$ is

• A. $\frac{3}{16}$
• B. $\frac{1}{32}$
• C. $\frac{1}{16}$
• D. $\frac{1}{8}$

Answer 1

The correct option is C $\frac{1}{16}$

$\cos 20\cos 40\cos 60\cos 80=\frac{2\sin {20}^{\circ }}{2\sin 20}\cos 20\cos 40\cos 60\cos 80$

$=\frac{\sin 40}{2\sin 20}\cos 40\cos 80\cos 60$

$=\frac{\sin {80}^{\circ }}{4\sin {20}^{\circ }}\cos {80}^{\circ }\cos {60}^{\circ }$

$=\frac{\sin {160}^{\circ }}{8\sin {20}^{\circ }}\cos {60}^{\circ }$

$=\frac{1}{8}\times \frac{1}{2}=\frac{1}{16}$

Hence, option 'C' is correct.