Question

cosx-sinx属于1到根号2的闭区间,求y=1-cosx+sinx+sinxcosx的值域

Answer 1

cosx-sinx=t (cosx-sinx)^2=1-2sinxcosx=t^2

sinxcosx=1-t^2/2

y=1-cosx+sinx+sinxcosx=1-t+(1-t^2)/2=-t^2/2-t+3/2=-1/2[t^2+2t+1]+2

对称轴t=-1

在【1,√2】上单调减

值域[1/2-√2,0]