不查表求{(1-cos20)/sin20-√3}*sin40有助于回答者给出准确的答案

Question

不查表求{(1-cos20)/sin20-√3}*sin40
有助于回答者给出准确的答案

Answer 1

(1-cos20)/sin20-√3
=(1-cos20-√3sin20)/sin20
=(1-2sin(20+30))/sin20
=(1-2sin50)/sin20
[(1-cos20)/sin20-√3]*sin40
=[(1-2sin50)/sin20]*2sin20cos20
=2[(1-2cos40)cos20]
=2[cos20-2cos40cos20]
=2cos20-2[cos(40+20)+cos(40-20)]
=-2cos60
=-1