Question

f(x)=根号下3cos^2（x+派/2）+1/2(sinx-cosx)^2,在[0.派/2]上的最大值为多少

Answer 1

f(x)=√3cos^2(x+π/2)+(1/2)(sinx-cosx)^2

=(√3/2)[1+cos(2x+π)]+cos^2(x+π/4)

=(√3/2)(1-cos2x)+(1/2)[1+cos(2x+π/2)]

=(√3+1)/2-cos2x-sin2x

=(√3+1)/2-√2sin(π/4+2x)

fmax(x)=(√3+1)/2+√2