Express cos4θ in terms of sinθ.

Question

I'm kind of stuck with this. My initial plan was to go from cos4θ to cos(2θ+2θ), which that wasn't ended well for some reason.

Sidenote: Please explain your answer, thank you!

Answer 1

You were going correct like

Cos(2theta+2theta)

Cos 2theta*cos2theta- sin2thetasin2theta (cos(a + b) = cos(a)cos(b) – sin(a)sin(b).)

Cos²2theta-sin²2theta

1-sin²2theta-sin²2theta

1-2sin²2theta

Hope it helped you