Question

The value of $\cos 1^{\circ }.\cos 2^{\circ }.\cos 3^{\circ }...\cos {179}^{\circ }$ is equal to:

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

Answer 1

The correct option is B $0$

We have:

$\cos 1^{\circ }.\cos 2^{\circ }.\cos 3^{\circ }.............\cos {179}^{\circ }$

$=$ $\cos 1^{\circ }.\cos 2^{\circ }.\cos 3^{\circ }...........\cos {90}^{\circ }.............\cos {179}^{\circ }$

$\therefore$ $\cos 1^{\circ }.\cos 2^{\circ }.\cos 3^{\circ }.............\cos {179}^{\circ }=0$ As $[\cos {90}^0=0]$