trigonometry How calculate cos of 165 (sum or difference of what angles)? cos(165)

We need to find
the values of cos(165).

We will need to rewrite the number (165) as a sum of
two known angles.

165 = 210 - 45   (210 is the angle 30 in the third
quadrant).

==> cos(165) = cos(210 - 45)

Now we will use
trigonometric identities to solve.

cos(210 - 45) = cos210*cos45 +
sin210*sin45

                     = -sqrt3/2 * sqrt2/2 +
(-1/2)*(sqrt2/2)

                     = -sqrt6/ 4 - sqrt2 /4

                     = (-sqrt6 - sqrt2)/4

                      =
-sqrt2(sqrt3 +1) /4

==> cos(165) = -sqrt2(sqrt3  +1) /
4