Evaluate cos 165.

We that cos (180 - A) = -cos
A.

cos ( 165) = cos( 180 - 15) = -cos
15.

cos 2A = (cos A)^2 - (sin
A)^2

= 2*(cos A)^2 - 1

cos 30
= 2* (cos 15)^2 - 1

sqrt 3/2 = 2*(cos 15)^2
-1

=> 2*(cos 15)^2 = 1 + sqrt
3/2

=> (cos 15)^2 = 1/2 + sqrt
3/4

=> (cos 15)^2 = (2 + sqrt
3)/4

=> cos 15 = sqrt (2 + sqrt 3)/
2

=> cos 165 = -sqrt (2 + sqrt 3)/
2

So cos 165 = -sqrt (2 + sqrt 3)/
2