Q. 123.8( 10 Votes )
Prove the following with the help of identities:
cos4θ + sin4θ = 1 – 2 cos2θ sin2θ
Answer :
Taking L.H.S we get,
Cos4 θ + sin4 θ
Using (a2 + b2) = (a + b)2 – 2.a.b
Where a = cos2 θ and b = sin2 θ
⇒ (cos2 θ + sin2 θ)2 – 2.cos2 θ.sin2 θ
⇒ 1 – 2.cos2 θ.Sin2 θ (Using: sin2 θ + cos2 θ = 1 )
= R.H.S
Hence, proved.
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