Cos^2-sin^2=1/3 so what is cos^4-sin^4

asked Jan 27, 2023 122k views

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Cos^2-sin^2=1/3
so what is cos^4-sin^4

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Explanation:

$cos ^(2) x - \sin ^(2) x = (1)/(3)$

$((cos ^(2)x - \sin ^(2) x)(cos ^(2)x + \sin ^(2) x))/((cos ^(2)x + \sin ^(2) x)) = (1)/(3)$

$((cos ^(4)x - \sin ^(4) x))/(1) = (1)/(3)$

as cos²x+sin²x=1

Hence

cos⁴x-sin⁴x=1/3

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