sin^4x-cos^4x
=(sin^2x-cos^2x)(sin^2x+cos^2x)
=sin^2x-cos^2x
=2sin^2x-1
tan^2x-sin^2x
=sin^2x/cos^2x-sin^2x
=(sin2x-sin^2xcos^2x)/cos^2x
=sin^4x/cos^2x
=tan^2xsin^2x
sin^4x-cos^4x
=(sin^2x-cos^2x)(sin^2x+cos^2x)
=sin^2x-cos^2x
=2sin^2x-1
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