Question 1190028
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Prove that sin^4 x - sin^2 x is equal to cos^4 x - cos^2 x
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Based on Trigonometry identity sin^2(x) + cos^2(x) = 1, we have

    sin^2(x) = 1 - cos^2(x)  and  cos^2(x) = 1 - sin^2(x).


Using it, we have this one line chain of equivalent transformations


{{{sin^4(x) - sin^2(x)}}} = {{{sin^2(x)*(sin^2(x) - 1)}}} = {{{-sin^2(x)*cos^2(x)}}} = {{{-(1-cos^2(x))*(cos^2(x))}}} = {{{cos^4(x)-cos^2(x)}}}.


and the proof is completed at this point.
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Solved.