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Prove that sin^4x=cos^4x+sin^2x-cos^2x?

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xav1394 | Student, Grade 11 | (Level 2) eNoter

Posted December 20, 2011 at 2:03 AM via web

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Prove that sin^4x=cos^4x+sin^2x-cos^2x?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted December 20, 2011 at 2:26 AM (Answer #1)

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Moving cos^4 x to the left side yields:

`sin^4 x - cos^4 x = sin^2 x- cos^2 x`

Using the formula of difference of squares to the left side yields:

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

Use the basic formula of trigonometry, `sin^2 x+ cos^2 x = 1` , such that:

`sin^4 x - cos^4 x = (sin^2 x- cos^2 x)*(1)`

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

The last line proves that the original identity is verified.

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