sin(x+pai/6)=1/4,sin(5/6pai-x)+sin^2(11/6pai-x)的值
问题描述：
sin(x+pai/6)=1/4,sin(5/6pai-x)+sin^2(11/6pai-x)的值
为
答
sin(x+pai/6)=1/4=sinxcospai/6+sinpai/6cosx=√3/2sinx+1/2cosx
,sin(5/6pai-x)+sin^2(11/6pai-x)=sin5/6paicosx-cos5/6paisinx+sin(2π-π/6-x)稍等sin(5π/6p-x)+sin^2(11/6pai-x)sin(x+π/6)=1/4=√3/2sinx+1/2cosx ,1- 2cosx=2√3sinx , 1-4cosx+4cos^2x=12sin^2x=12-12cos^2x
16cos^2x-4cosx-11=0 , 16(cosx-1/8)^2-45/4=0 , cosx=1/8±3√5/8
sin(5π/6p-x)+sin^2(11π/6-x)=sin[π-(π/6+x)]+sin^2[2π-(π/6-x)]
=sin(π/6+x)-sin(π/6-x)
=√3/2sinx+1/2cosx-(√3/2sinx-1/2cosx)
=cosx
=1/8±3√5/8