Question

How do you express cos(4θ) in terms of cos(2θ) using the double angle identity?

Answer 1

`cos2x = cos^2x -sin^2x`

Accordingly, `cos4x = cos^2 2x -sin^2 2x`

Expressing cos(4θ) in terms of cos(2θ)

`cos(4θ) = cos^2 2theta -sin^2 2theta`

`cos(4θ) = cos^2 2theta -(1-cos^2 2theta)`

`cos(4θ) = 2cos^2 2theta -1`