Question

prove that cos12+cos84+cos132+cos156=-1/2

Answer 1

=cos132 + cos 12 + cos 84 + cos 156
=2cos72cos60+2cos120cos36
=2{(root5-1)/4}1/2 + 2(-1/2)(root5+1)/4
=-1/2
pls mark it as brainliest.

Answer 2

Given cos 12 + cos 84 + cos 132 + cos 156 can be written as

           cos 156 + cos 84 + cos 132 + cos 12

We know that cos a + cos b = 2 cos(a+b)/2 cos (a-b)/2

       =  2 cos(156 + 84/2) cos (156 - 84/2)  + 2 cos(132 + 12/2) cos(132 - 12/2)

       =  2 cos 120 cos 36 + 2 cos 72 cos 60

      = 2 * -1/2 cos 36 + 2 * 1/2 * cos 72

      = cos 72 - cos 36

     = -1/2