sin^4 theta -cos^4 theta in terms of sec
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sin^4θ- cos ^4 θ
= (sin ^2 θ)^2- (cos ^2θ)^2
=(sin^2θ + cos ^2θ)( sin^2 θ - cos^2θ)
= 1*(1- cos^2 θ -cos^2 θ) [here sin^2 θ = 1- cos^2θ]
= 1- 2cos^2 θ
= 1 - 2/ sec^2 θ [since cos θ = 1/sec θ]
= (sin ^2 θ)^2- (cos ^2θ)^2
=(sin^2θ + cos ^2θ)( sin^2 θ - cos^2θ)
= 1*(1- cos^2 θ -cos^2 θ) [here sin^2 θ = 1- cos^2θ]
= 1- 2cos^2 θ
= 1 - 2/ sec^2 θ [since cos θ = 1/sec θ]
mysticd:
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