Question

How do you simplify the following expression?

`cos4x cos2x-sin4xsin2x`

Answer 1

`cos(4x)cos(2x)-sin(4x)sin(2x)=cos(6x)`

Explanation:

By the angle sum identity

`cos(theta_1+theta_2)=cos(theta_1)cos(theta_2)-sin(theta_1)sin(theta_2)`

Notice this is equivalent to the equation

`cos(4x)cos(2x)-sin(4x)sin(2x)`

If we choose `theta_1=4x` and `theta_2=2x`

Therefore we can simplify as

`cos(6x)`