Question

XVerify the identity. (7 points) cos 4u = cos22u - sin22u

Answer 1

cos 4u = co^s2 2u - sin^2 2u

Explanation:

cos 4u = co^s2 2u - sin^2 2u

Let 4u = 2x

cos 2x = cos^2 x - sin^ 2 x

cos (x+x) = cos^2 x - sin^ 2 x

Using cos(x+y) = cos(x)cos(y) -sin(x)sin(y)

cos(x) cos(x)- sin(x) sin (x)= cos^2 x - sin^ 2 x

cos^2 (x) -sin^2 (x) =cos^2 x - sin^ 2 x

Since this is true

cos 2x = cos^2 x - sin^ 2 x

This is true

Substituting 4u back for 2x

cos 4u = co^s2 2u - sin^2 2u

This is true