sin40°*(1-sin10°)/[sin10°*(cos20°)^2]

题目

sin40°*(1-sin10°)/[sin10°*(cos20°)^2]
2*根号3

答案

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