一个高中数学题,数学高手进!

siny,sin2x,cosy成等差数列
2sin2x=siny+cosy
siny,sinx,cosy 成等比数列
sin^2x=sinycosy,
而,(siny+cosy)^2-2sinycosy=sin^2y+cos^2y=1
所以(2sin2x)^2-2sin^2x=1
4(sin2x)^2-1+cos2x-1=0
4-4(cos2x)^2+cos2x-2=0
4(cos2x)^2-cos2x-2=0
cos2x=(1±根号33)/8

Sin@,Sin2x,Cos@成等差数列
2Sin2x=Sin@+Cos@
4Sin2x^2=1+2Sin@Cos@
Sin2x^2=(1+2Sin@Cos@)/4
Sin@,Sinx,Cos@成等比数列
Sinx^2=Sin@Cos@
Cos2x=1-2Sinx^2=1-2Sin@Cos@
Sin2x^2+Cos2x^2=1
Cos2x=(1+√33)/8或(1-√33)/8