resolva 〖sen〗^4x+〖cos〗^4 x=3/4?

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sin(x)^4 + cos(x)^4 = 3/4
(sin(x)^2)^2 + cos(x)^4 = 3/4 ... write 4th power as square of a square
(1 - cos(x)^2)^2 + cos(x)^4 = 3/4 ... substitute for sin^2
1 - 2cos(x)^2 + cos(x)^4 + cos(x)^4 = 3/4 ... eliminate parentheses
1 - 2cos(x)^2(1 - cos(x)^2) = 3/4 ... factor cosine terms
1 - 2cos(x)^2·sin(x)^2 = 3/4 ... substitute for cos^2
1 - sin(2x)^2/2 = 3/4 ... substitue 2sin(x)cos(x) = sin(2x)
(1 + 1 - sin(2x)^2)/2 = 3/4 ... rewrite to common denominator
(1 + cos(2x)^2)/2 = 3/4 ... substitute for sin^2
(1 + (1 + cos(4x))/2)/2 = 3/4 ... substitute for cos^2, double angle formula
(3/4) + cos(4x)/4 = 3/4 ... simplify
cos(4x) = 0 ... subtract 3/4, multiply by 4

Solutions are x = (2n+1)π/8 for any integer n.