How do you verify the identity $sin^2alpha-sin^4alpha=cos^2alpha-cos^4alpha$ ?

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Answer 1 · 2017-02-26T20:21:19

$"please look at the fallowing solution."$

$sin^2 alpha-sin^4 alpha=color(red)(cos^2 alpha-cos^4 alpha)$

$"let " sin^2 alpha -sin^4 alpha =k$

$sin^2 alpha=1-cos^2 alpha$

$sin^4 alpha=(1-cos^2 alpha)^2=1-2 cos^2 alpha+ cos^4 alpha$

$k=1-cos^2 alpha-(1-2cos^2 alpha +cos^4 alpha)$

$k=cancel(1)-cancel(cos^2) alpha cancel(-1)+cancel(2cos^2) alpha -cos^4 alpha$

$k=color(red)(cos^2 alpha-cos^4 alpha)$

How do you verify the identity sin^2alpha-sin^4alpha=cos^2alpha-cos^4alphasin^2alpha-sin^4alpha=cos^2alpha-cos^4alpha?