Question

Find the value of $\cos 1^{\circ }\cos 2^{\circ }\cos 3^{\circ }......\cos {180}^{\circ }$

• A. $1$
• B. $-1$
• C. $0$
• D. None of these

Answer 1

The correct option is C

$0$

Explanation for the correct answer:

Find the value of $\cos 1°\cos 2°\cos 3°......\cos 180°$

The value of $cos\theta$ lies between $-1$ and $1$

We also know that,

$\cos 0°=1$

$cos90°=0$ and

$cos180°=-1$

Since $\cos 90°=0$ is one of the terms in the product of given equation

so the final product will be $0$

Hence the value of $\cos 1°\cos 2°\cos 3°......\cos 180°$is $0$.

Hence, option (C) is the correct answer