Q. 123.8( 10 Votes )

# Prove the following with the help of identities:

cos^{4}θ + sin^{4}θ = 1 – 2 cos^{2}θ sin^{2}θ

Answer :

Taking L.H.S we get,

Cos^{4} θ + sin^{4} θ

Using (a^{2} + b^{2}) = (a + b)^{2} – 2.a.b

Where a = cos^{2} θ and b = sin^{2} θ

⇒ (cos^{2} θ + sin^{2} θ)^{2} – 2.cos^{2} θ.sin^{2} θ

⇒ 1 – 2.cos^{2} θ.Sin^{2} θ (Using: sin^{2} θ + cos^{2} θ = 1 )

= R.H.S

Hence, proved.

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