y=sin（x+pai/18）cos(x+2pai/9)的最小值

y=sin（x+pai/18）cos(x+2pai/9)的最小值
y=sin（x+pai/18）cos(x+2pai/9)的最小值

y=sin（x+pai/18）cos(x+2pai/9)的最小值
y=sin（x+pai/18）cos(x+2pai/9)
=1/2（ sin(x+x+2π/9+π/18)-sin(2π/9-π/18)）
=1/2(sin(2x+（5π /18)）-sinπ/6）
=1/2（sin(2x+（5π /18))-1/2)
=1/2sin(2x+（5π /18))-1/4
当sin(2x+（5π /18))=-1时,y达到最小值=-1/2-1/4=-3/4

y=sin（x+pai/18）cos(x+2pai/9)
=sin(x+π/18)cos[(x+π/18)+3π/18]
=sin(x+π/18)[根号3/2sin(x+π/18)cos(x+π/18-1/2sin^2(x+π/18）
=(用二倍角公式）1/2[根号3/2sin(2x+π/9）+1/2cos(2x+π/9）-1/2]
=1/2[sin(2x+π/9+π/6）-1/2]
sin(2x+5π/18）=-1 时候 y=1/2[sin(2x+5π/18）-1/2]=-3/4