Solution
Apply the angle-sum identity for cosine to cos(x+x).
Explanation:
The identity needed is the angle-sum identity for cosine.
cos(α+β)=cos(α)cos(β)−sin(α)sin(β)
With that we have
cos)2x=cos(x+x)
=cos(x)cos(x)−sin(x)sin(x)
=cos
2
(x)−sin
2
(x)