Q12 of 48 Page 84

Prove the following with the help of identities:

cos4θ + sin4θ = 1 – 2 cos2θ sin2θ

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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