Q. 17 B4.3( 25 Votes )

# 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.

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