Let f (x) = (SiNx) ^ 4-sinxcosx + (cosx) ^ 4, then the range of F (x) is

(SiNx) ^ 4 + (cosx) ^ 4 = [(SiNx) ^ 2 + (cosx) ^ 2] ^ 2-2 (SiNx) ^ 2 * (cosx) ^ 2 = 1 ^ 2-2 (SiNx) ^ 2 * (cosx) ^ 2 = 1-2 (sinxcosx) ^ 22sinxcosx = sin2x, so (SiNx) ^ 4 + (cosx) ^ 4 = 1 - (sin2x) ^ 2 / 2, so f (x) = - (sin2x) ^ 2 / 2 - (sin2x) / 2 + 1 let a = sin2x, then - 1

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