Express cos4θ and sin4θ in terms of sines and cosines of multiples of θ

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Express cos4θ and sin4θ in terms of sines and cosines of multiples of θ.

Using a trignometric identity:
cos (2θ) = cos^2(θ) - sin^2(θ)

Since 4θ = 2*2θ, so we have:
cos(4θ) = cos^2(2θ) - sin^2(2θ)

Using another trignometric identity, we have:
sin(2θ) = 2 sin(θ) cos(θ)

Since 4θ = 2*2θ, so we have:
sin(4θ) = 2 sin(2θ) cos(2θ)