1.

\begin { equation } \cos ^{4} \theta-\sin ^{4} \theta=2 \cos ^{2} \theta-1=1-2 \sin ^{2} \theta \end { equation }

Answer»

We know that

cos(2θ)=cos^2(θ)−sin^2(θ)cos(2θ)=1⋅(cos^2(θ)−sin^2(θ))cos(2θ)=(cos^2(θ)+sin^2(θ))(cos^2(θ)−sin^2(θ))[sincesin^2θ+cos^2θ=1]cos(2θ)=cos^4(θ)−sin^4(θ)[since(a+b)(a−b)=a^2−b^2]

Hence proved



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