Find the exact value of the following expression which basic

Find the exact value of the following expression which basically stands for the sum of cos1° , cos2° ,cos3° all the way up to cos179°.

Solution

cos1 degree =cos(90-89 )=sin 89 degree

cos2degree=cos(90-88)=sin 88 degree

cos3degree=cos(90-87)=sin 87 degree

Threfore the answer is

sin 89 degree, sin 88 degree, sin 87 degree, sin 86 degree, ......