若x,y为锐角,cosx=3/5,cos(x+y)=根号3/3,求siny的值

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若x,y为锐角,cosx=3/5,cos(x+y)=根号3/3,求siny的值
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若x,y为锐角,cosx=3/5,cos(x+y)=根号3/3,求siny的值
若x,y为锐角,cosx=3/5,cos(x+y)=根号3/3,求siny的值

若x,y为锐角,cosx=3/5,cos(x+y)=根号3/3,求siny的值
x,y为锐角,cosx=3/5,cos(x+y)=√3/3
则由平方关系可得:sinx=4/5,sin(x+y)=√6/3
则:siny=sin[(x+y)-x]
=sin(x+y)cosx-cos(x+y)sinx
=(√6/3)(3/5)-(√3/3)(4/5)
=(3√6-4√3)/15

x,y为锐角,cosx=3/5,cos(x+y)=根号3/3
所以sinx=4/5,sin(x+y)=根号6/3
siny=sin[(x+y)-x]
=sin(x+y)cosx-cos(x+y)sinx
=(根号6/3)*(3/5)-(根号3/3)*(4/5)
=(3根号6-4根号3)/15