Question

How do you verify `cos(4θ) = (2cos^4θ) − (4cos^2θ) (sin^2θ) + 2sin^4θ − 1`?

Answer 1

`cos(4theta)`

`=2cos^2(2theta) -1 color(white)("xxxxxx") "since" cos(2x) = 2cos^2(x) -1`

`=2(cos^2(theta) - sin^2(theta))^2 -1 color(white)("xxxxxx") "since" cos(2x) = cos^2(x)-sin^2(x)`

`= 2(cos^4(theta) - 2cos^2(theta)sin^2(theta) + sin^4(theta) -1`

`= 2cos^4(theta) - 4cos^2(theta)sin^2(theta) + 2sin^4(theta) -1`