sin40°*(1-sin10°)/[sin10°*(cos20°)^2]

sin40°(1-sin10°)/[sin10°(cos20°)^2]
=2sin20°cos20°(1-cos80°)/ [sin10°(cos20°)^2]
=2sin20°(sin40°)^2/(sin10°cos20°)
=2sin20°(2cos20°sin20°)^2/(sin10°cos20°)
=16cos10°cos20°(sin20°)^3/(2sin10°cos10°)
=16cos10°cos20°(sin20°)^2
=8sin80°sin40°sin20°
=4(cos40°-cos120°)sin20°
=4(cos40°sin20°+1/2sin20°)
=4(1/2sin60°-1/2sin20°+1/2sin20°)
=4sin60°
=2√3

sin40°*(1-sin10°)/[sin10°*(cos20°)^2]
=sin40*(1-cos80)/(sin10*cos^2 20)
=2*sin40*(sin40)^2/(sin10°*(cos20°)^2)
=2*(sin40)^3/(sin10°*(cos20°)^2)=16*(cos20*sin20)^3/(sin10°*(cos20°)^2)=32*cos20(sin20)^2cos10=16*sin40sin20sin10
设A=sin40sin20sin10
A=1/2*(cos20-cos60)sin10=1/2*(cos20sin10-1/2sin10)=1/2*(1/2*sin30+1/2*sin10-1/2*sin10)=1/4*sin30

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