求6/5（sinθ+cosθ）-sinθ*cosθ的最大值和最小值

题目

求6/5（sinθ+cosθ）-sinθ*cosθ的最大值和最小值
0＜θ＜90°

答案

原式=6/5[sinθ+sin(π/2-θ)]- sin(2θ)/2=12/5[sin(π/4) cos(θ-π/4)]- sin(2θ)/2=6√2/5 cos(θ-π/4)-cos(2θ-π/2)/2=6√2/5 cos(θ-π/4)-{2 [cos(θ-π/4)]^2-1}/2=-[cos(θ-π/4)]^2+6√2/5 cos(θ-π/4)...