解方程：sinx+2sin2x=3+sin3x.

sinx+2sin2x=3+sin3x
sinx-sin3x+2sin2x=3
sin(2x-x)-sin(2x+x)+2sin2x=3
-2sinxcos2x+2sin2x=3
sin2x-sinxcos2x=3/2
后面可以这样：
2sinxcosx-sinx(2cosx平拆则方-1）码哪=3/2
2sinx（cosx-2cosx平方+1)=3/2
sinx(-（osx-1/2)平方-3/4）=3/2
第一项不大于1第二项不大迟御码于3/4 且二者不能同时达到.故右边小于3/2

sin3x =3*sinx*cosx^2 - sinx^3
sinx+2sin2x=3+sin3x
sinx-sin3x+2sin2x=3
sin(2x-x)-sin(2x+x)+2sin2x=3
-2sinxcos2x+2sin2x=3
sin2x-sinxcos2x=3/2
cos2x>0时
(sin2x-cos2x)√2sin(2x-π/4)√2sin(2x+π/4)<3/2,√2sin(2x-π/4)<3/2
方程无解
cos2x<0时，
(sin2x+cos2x)<埋磨局sin2x-sinxcos2x<(sin2x-cos2x)
√2sin(2x+π/4)√2sin(2x+π/4)<3/2,√2sin(2x-π/4)<3/2
方游带程无解

sinx+2sin2x=3+sin3x
sinx-sin3x+2sin2x=3
sin(2x-x)-sin(2x+x)+2sin2x=3
-2sinxcos2x+2sin2x=3
sin2x-sinxcos2x=3/2
cos2x>0时
(sin2x-cos2x)<顷拍sin2x-sinxcos2x<(sin2x+cos2x)
√2sin(2x-π/4)√2sin(2x+π/4)<3/2,√2sin(2x-π/4)<3/2
方程无解
cos2x<0时，
(sin2x+cos2x)√2sin(2x+π/4)√雀笑羡2sin(2x+π/4)<3/2,√2sin(2x-π/4)<3/2
方程无解