已知f(x)=sin平方x+sinxcosx.x∈[0,pai/2]

题目

已知f(x)=sin平方x+sinxcosx.x∈[0,pai/2]
求f(x)的值域,若f(a)=5/6,求sin2a的值

答案

f(x)=(sinx)^2+sinxcosx=[cos(2x)-1]/2+sin(2x)/2=(1/2)[sin(2x)+cos(2x)]-1/2=(√2/2)sin(2x+π/4)-1/2x∈[0,π/2]2x+π/4∈[π/4,5π/4]sin(2x+π/4)∈[-√2/2,1]当sin(2x+π/4)=1时,f(x)有最大值f(x)max=(√2-1)/...