sinx siny=根號2/2 cosx cosy=根號6/2 則sin（x y）=網友廻答：
- sinx siny＝√2/2→2sin[(x y)/2]cos[(x-y)/2]＝√2/2;
cosx coy＝√6/2→2cos[(x y)/2]cos[(x-y)/2]＝√6/2.
兩式相除，得tan[(x y)/2]＝√3/3.
∴依萬能公式，得sin(x y)＝2×(√3/3)/[1 (√3/3)²]＝√3/2。
網友廻答：
- sinx siny=根號2/2
sin^2x sin^2y 2sinxsiny=1/2.......(1)
cosx cosy=根號6/2
cos^2x cos^2y 2cosxcosy=3/2....(2)
(1) (2)得
2 2cos(x-y)=2
cos(x-y)=0
x=y
sinx=根號2/4,cosx=根號6/4
sin（x y)=sin2x=2sinxcosx=2*根號2/4*根號6/4=根號3/4
網友廻答：
- sinx siny=√2/2,cosx cosy=√6/2； 則sin(x y)=
由sinx siny=√2/2得sin²x 2sinxsiny sin²y=1/2.(1)
由cosx cosy=√6/2得cos²x 2cosxcosy cos²y=3/2.(2)
(1) (2)得2 2(cosxcosy sinxsiny)=2 2cos(x-y)=2,故cos(x-y)=0；
(2)-(1)得cos²x-sin²x 2(cosxcosy-sinxsiny) cos²y-sin²y=1
即有cos2x 2cos(x y) cos2y=2cos(x y) cos2x cos2y
=2cos(x y) 2cos(x y)cos(x-y)=2cos(x y)=1；
故cos(x y)=1/2,x y=π/3 2kπ.
∴sin(x y)=sin(2kπ π/3)=sin(π/3)=√3/2.
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