1 求sin10sin50sin70的值 2:若tan(π|4-α)=3,则cotα等于

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1求sin10sin50sin70的值2:若tan(π|4-α)=3,则cotα等于1求sin10sin50sin70的值2:若tan(π|4-α)=3,则cotα等于1求sin10sin50sin7

1 求sin10sin50sin70的值 2:若tan(π|4-α)=3,则cotα等于
1 求sin10sin50sin70的值 2:若tan(π|4-α)=3,则cotα等于

1 求sin10sin50sin70的值 2:若tan(π|4-α)=3,则cotα等于
1 .sin10sin50sin70=cos10sin10sin50sin70/cos10
=[1/2(sin20cos20cos40)]/cos10
=(1/4sin40cos400/cos10
=(1/8sin80)/cos10
=1/8
2 .tan-α=tan[(π|4-α)-π|4]=[tan(π|4-α)-tan(π|4)]/1+tan(π|4-α)
=1/2
所以tanα=-1/2
cotα等于1/tanα=-2

1、sin10sin50sin70=cos80`cos40`cos20`=sin20`cos20`cos40`cos80`/sin20`
=(1/2)sin40`cos40`cos80`/sin20`=(1/4)sin80`cos80`/sin20`=(1/8)sin160`/sin20`=(1/8)sin(180`-20`)/sin20`=(1/8)sin20`/sin20`=1/8
2、tan(π/4-α)=3=(1-tana)/(1+tana),tana=-1/2
cota=-2