设X属于｛0,π/2｝.f（x）=sin(cosX),g（x）=cos（sinx）求f（x）和g（x）的最大值和最小值.

y=sin^2(x) 2sinxcosx 3cos^2(x) =sin^2(x) cos^2(x) 2sinxcosx 2cos^2(x) =1 sin2x 2cos^2(x) =2 sin2x (2cos^2(x)-1) =sin2x cos2x 2 =√2(sin2x*(√2/2) cos2x*(√2/2)) 2 =√2(sin(2x (π)/4) 2 由正弦函数y=sinx的值域[-1,1] ① 最大值：当x=(π/2) 2kπ时,y(max)=1 ②最小值：当x=-(π/2) 2kπ时,y(min)=-1,在[-(π/2) 2kπ,(π/2) 2kπ]上是增函数,在[(π/2) 2kπ,(3π/2) 2kπ]上是减函数 可得,它的最大值是当x=(π/8) kπ时,y(max)=√2 2