Question

The sum $\cos 1^o+\cos 2^o+\cos 3^o+....+\cos {179}^o+\cos {180}^o$ is equal to:

• A. $0$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

Answer: (C)

$-1$

The sum$\cos 1^{\circ }+\cos 2^{\circ }+.........\cos {179}^{\circ }+\cos {180}^{\circ }$is equal to:

$=\cos 1^{\circ }+\cos 2^{\circ }+.......\cos {90}^{\circ }.......+\cos {179}^{\circ }+(-1)$

$=\cos (180-179)+\cos (180-178)+....\cos {90}^{\circ }+....\cos {178}^{\circ }+\cos {179}^{\circ }-1$

$=-\cos {179}^{\circ }-\cos {178}^{\circ }+......\cos {90}^{\circ }+.....\cos {178}^{\circ }+\cos {179}^{\circ }-1$

Post cancelling,

$=-1$