∵a•b=-(cosx)^2+sinxcosx
=-(1+cos2x)/2+sin2x/2
=(sin2x-cos2x)-1/2
=√2[(√2/2)sin(2x)-√2/2cos(2x)]-1/2
=√2sin(2x-π/4)-1/2
∴2ab+1=2√2sin(2x-π/4)
又∵x∈(π/2,9π/8)
∴f(x)的最大值为2,此时x=π/2
题目可能出错了 x应该∈[π/2,9π/8]
∵a•b=-(cosx)^2+sinxcosx
=-(1+cos2x)/2+sin2x/2
=(sin2x-cos2x)-1/2
=√2[(√2/2)sin(2x)-√2/2cos(2x)]-1/2
=√2sin(2x-π/4)-1/2
∴2ab+1=2√2sin(2x-π/4)
又∵x∈(π/2,9π/8)
∴f(x)的最大值为2,此时x=π/2
题目可能出错了 x应该∈[π/2,9π/8]