Question

Write the given expression as the cosine of an angle: cos60cos105 - sin60sin105?

Answer 1

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°)