求函数y=sin(x+20)-cos(x+50)最大值

y=sin(x+20)-cos(x+50)
=sin(x+20)-cos(x+20)cos30+sin(x+20)sin30
=3/2sin(x+20)-根号3/2cos(x+20)
=根号3[根号3/2sin(x+20)-1/2cos(x+20)]
=根号3[cos30sin(x+20)-sin30cos(x+20)]
=根号3sin(x-10)
Ymax=根号3

y=sin(x+20)-cos(x+50)
=sin(x+20)-cos(x+20)cos30+sin(x+20)sin30
=sin(x+20)-cos(x+20)根号3/2+sin(x+20)/2
=3sin(x+20)/2-根号下{3[1-sin(x+20)^2]}/2
设sin(x+20)=a
则y=3a/2-根号下[3(1-a^2)]/2
-1要使y最大
取a=1
y=3/2

这里把20,50当成普通的度数来看待吧?
y=sin(x+20)-sin(40-x)=2cos30sin(x-10)=√3sin(x-10)
当x=100度时取最大值√3.

y=sin(x+20)-sin(40-x)=2cos(30)sin(x-10) （和差化积）
所以最大值为2cos(30)=√3