Question

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

Answer 1

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