Prove that sin^4x=cos^4x+sin^2x-cos^2x?
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sciencesolve | Teacher | (Level 3) Educator Emeritus
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.