we know that
The cosine of the sum of two angles is defined by the following trigonometric identity
cos(A + B) = cos A cos B − sin A sin B
A=60°
B=105°
cos A=cos 60
cos B=cos 105
sin A=sin 60
sin B=sin 105
then
cos(60 + 105) = cos 60 cos 105 − sin 60 sin 105
cos(165) = cos 60 cos 105 − sin 60 sin 105
the answer is
cos (105°)
