Question

The value of $\cos {20}^o\cos {40}^o\cos {80}^o$ is equal to

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

Answer 1

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

according to question,

$\Rightarrow \cos {20}^{\circ }\cos {40}^{\circ }\cos {80}^{\circ }=\frac{1}{4}\cos {60}^{\circ }$

$=\frac{1}{8}$

Now,

$\Rightarrow \cos \theta \cos \left({60}^{\circ }-\theta \right)\cos \left({60}^{\circ }+\theta \right)=\frac{1}{4}\cos 3\theta$

hence, option $C$ is correct.