求助！！为什么cos(π/5)-cos(2π/5)=1/2 ?
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cos(π/5)-cos(2π/5)
=cos(π/5)+cos(3π/5)
=cos(2π/5-π/5)+cos(2π/5+π/5)
=cos(2π/5)*cos(π/5)+sin(2π/5)*sin(π/5)+cos(2π/5)*cos(π/5)-sin(2π/5)*sin(π/5)
=2cos(2π/5)*cos(π/5)
=2sin(π/10)*cos(π/5)
=sin(π/5)*cos(π/5)/cos(π/10)
=(1/2)sin(2π/5)/cos(π/10)
=(1/2)cos(π/10)/cos(π/10)
=1/2
=cos(π/5)+cos(3π/5)
=cos(2π/5-π/5)+cos(2π/5+π/5)
=cos(2π/5)*cos(π/5)+sin(2π/5)*sin(π/5)+cos(2π/5)*cos(π/5)-sin(2π/5)*sin(π/5)
=2cos(2π/5)*cos(π/5)
=2sin(π/10)*cos(π/5)
=sin(π/5)*cos(π/5)/cos(π/10)
=(1/2)sin(2π/5)/cos(π/10)
=(1/2)cos(π/10)/cos(π/10)
=1/2
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