若x属于(0,π/4),求函数y=cos^2x-sin^x+2sinxcosx的值域

问题描述:

若x属于(0,π/4),求函数y=cos^2x-sin^x+2sinxcosx的值域

y=cos2x+sin2x
=√2(√2/2*cos2x+√2/2sin2x)
=√2(sinπ/4cos2x+cosπ/4sin2x)
=√2sin(π/4+2x)
0