Q. 17 B4.3( 25 Votes )

# Prove each of the following identities:

sin^{2} θ + cos^{4}θ = cos^{2} θ + sin^{4} θ

Answer :

Consider L.H.S. = sin^{2} θ + cos^{4} θ

= (sin^{2} θ) + (cos^{2} θ)^{2}

= (sin^{2} θ) + (1 – sin^{2} θ)^{2}

= (sin^{2} θ) + 1 + sin^{4} θ – 2sin^{2} θ

= 1 – sin^{2} θ + sin^{4} θ

= cos^{2} θ + sin^{4} θ

= R.H.S.

Hence, proved.

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