Question

The value of the expression $\cos \left(1°\right)·\cos \left(2°\right)·...·\cos \left(179°\right)$ is

• A. $0$
• B. $1$
• C. $\frac{1}{\sqrt{2}}$
• D. $-1$

Answer 1

The correct option is A

$0$

Explanation for correct option :

Given trigonometric expression is $\cos \left(1°\right)·\cos \left(2°\right)·...·\cos \left(179°\right)$

$\begin{array}{rcl}\therefore \cos \left(1°\right)·\cos \left(2°\right)·...·\cos \left(179°\right)& =& \cos \left(1°\right)·\cos \left(2°\right)·...·\cos \left(89°\right)·\cos \left(90°\right)·\cos \left(91°\right)·...·\cos \left(179°\right)\\ & =& 0\left[\because \cos \left(90°\right)=0\right]\end{array}$

Hence, option (A) is correct.