已知sinx=7分之4倍根号3,sin(x-y)=14分之3倍根号3,且1＜y＜x＜2分之π,求y的值

已知sinx=7分之4倍根号3,sin(x-y)=14分之3倍根号3,且1＜y＜x＜2分之π,求y的值
已知sinx=7分之4倍根号3,sin(x-y)=14分之3倍根号3,且1＜y＜x＜2分之π,求y的值

已知sinx=7分之4倍根号3,sin(x-y)=14分之3倍根号3,且1＜y＜x＜2分之π,求y的值
cosx=1/7
cos(x-y)=13/14
siny
=sin(x-(x-y))
=sinxcos(x-y)-cosxsin(x-y)
=4√3/7*13/14-1/7*3√3/14
=√3/2
所以y=π/3

Y=sin x+√3sinxcosx =(1-cos(2x))/2+√3/2*sin(2x) =√3/2*sin(2x) -cos(2x)/2+1/2 = sin(2x-π/6) +1/2 X∈[π/4, π/