Answer:
cos(x -π/3) = (1/2)cos(x) +(√3/2)sin(x)
Explanation:
You want cos(x -π/3) written in terms of sine and cosine.
Angle difference
The formula for the cosine of the difference between two angles is ...
cos(a -b) = cos(a)cos(b) +sin(a)sin(b)
Application
We have a=x, b=π/3, so the desired function is ...
cos(x -π/3) = cos(x)cos(π/3) +sin(x)sin(π/3)
We know that ...
- cos(π/3) = 1/2
- sin(π/3) = √3/2
so the rewrite is ...
cos(x -π/3) = (1/2)cos(x) +(√3/2)sin(x)