Prove each of the following identities:
sin2 θ + cos4θ = cos2 θ + sin4 θ
Consider L.H.S. = sin2 θ + cos4 θ
= (sin2 θ) + (cos2 θ)2
= (sin2 θ) + (1 – sin2 θ)2
= (sin2 θ) + 1 + sin4 θ – 2sin2 θ
= 1 – sin2 θ + sin4 θ
= cos2 θ + sin4 θ
= R.H.S.
Hence, proved.