Question

已知函数f(x)=1/2cosx方-根号sinxcosx-1/2sinx方+1(x属于R）

Answer 1

①化简f（x）=1+sin(π/6-2x)

∴T=2π/w=π π/6-2x∈[-5/6π,π/6] f(x)min=1-1=0 f(x)max=1+1/2=3/2

②得sin(π/6-2x)=4/5 π/6-2x∈[-π/6,π/2]

cos2x=cos(π/6-2x-π/6)=cos(π/6-2x)cos(π/6)+sin(π/6-2x)sin(π/6)=3/5 * √3/2 + 4/5 * 1/2 = (4+3√3)/10