Q6 of 45 Page 131

Prove that:

sin4 θ – cos4 θ = 1 – 2cos2 θ

L.H.S = sin4θ – cos4θ


= (sin2θ – cos2θ)(sin2θ + cos2θ)


= (sin2θ – cos2θ)


= (1 – cos2θ – cos2θ)


= 1- 2cos2θ


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