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How to prove that: `sin^2xcos^3x=(sin^2x-sin^4x)cosx`

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farajallah | eNotes Newbie

Posted April 30, 2013 at 2:05 PM via web

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How to prove that:

`sin^2xcos^3x=(sin^2x-sin^4x)cosx`

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oldnick | Valedictorian

Posted April 30, 2013 at 2:20 PM (Answer #1)

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`sin^2xcos^3x=sin^2x(1-sin^2x)cosx=(sin^2x-sin^4x)cosx`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 30, 2013 at 2:25 PM (Answer #2)

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The identity `sin^2xcos^3x=(sin^2x-sin^4x)cosx` has to be proved.

Start with the left hand side

`sin^2xcos^3x`

= `sin^2x*cos^2x*cos x`

= `sin^2x*(1 - sin^2x)*cosx`

= `(sin^2x - sin^4x)*cos x`

This proves that `sin^2xcos^3x=(sin^2x-sin^4x)cosx`

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