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y = (sinx)^4 + (cosx)^4 = [(sinx)^2 + (cosx)^2]^2 - 2(sinxcosx)^2
= 1 - 2(sinxcosx)^2
= 1 - 1/2 (sin2x)^2
= 1 - 1/4 (1-cos4x)
= 3/4 + (cos4x)/4
n≥1：
y(n) = [ 3/4 + (cos4x)/4 ](n)
=[ 3/4 ](n) + 1/4 [ (cos4x)(n) ]
= 1/4 [ 4^n cos(4x+ nπ/2)]
= 4^(n-1) cos(4x+ nπ/2)
= 1 - 2(sinxcosx)^2
= 1 - 1/2 (sin2x)^2
= 1 - 1/4 (1-cos4x)
= 3/4 + (cos4x)/4
n≥1：
y(n) = [ 3/4 + (cos4x)/4 ](n)
=[ 3/4 ](n) + 1/4 [ (cos4x)(n) ]
= 1/4 [ 4^n cos(4x+ nπ/2)]
= 4^(n-1) cos(4x+ nπ/2)
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