Question

The value of $(\cos 1^o+\cos 2^o+\cos 3^o+...+\cos {180}^o)$ is__________

Answer 1

Given,

$\cos 1^o+\cos 2^o+...........+\cos {178}^o+\cos {179}^o+\cos {180}^o$

$=\cos 1^o+\cos 2^o+...........+\cos ({180}^o-2^o)+\cos ({180}^o-1^o)+\cos {180}^o$

$=\cos 1^o+\cos 2^o+...........-\cos 2^o-\cos 1^o+\cos ({180}^o-0^o)$................................$\because cos({180}^0-\theta )=-cos\theta$

$=-\cos 0^o$

$=-1$