sin^2 10°+ sin^2 50°+ sin10°sin50°计算 ,

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sin^2 10°+ sin^2 50°+ sin10°sin50°计算 ,
sin^2 10°+ sin^2 50°+ sin10°sin50°
计算 ,

sin^2 10°+ sin^2 50°+ sin10°sin50°计算 ,
3/4.
sin^2 10°+ sin^2 50°+ sin10°sin50°
=(1-cos20)/2+(1-cos100)/2+(cos40-cos60)/2
=(2-cos20-cos60+cos100+cos40)/2
=(2-cos20-cos60+2cos60cos20)/2
=(2-cos20-cos60+cos20)/2
=(2-1/2)/2
=3/4

sin^2 10°+ sin^2 50°+ sin10°sin50°
=(sin10+sin50)^2
=(sin10+sin(60-10))^2
=(1/2sin10+根号3/2cos10)^2
=sin(10+60)^2
=(1-cos140)/2
=(1+cos40)/2