cos²α+cos²(120°-α)+cosαcos(120°-α)化简cos²α+cos²(120°-α)+cosαcos(120°-α)
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cos²α+cos²(120°-α)+cosαcos(120°-α)化简cos²α+cos²(120°-α)+cosαcos(120°-α)
cos²α+cos²(120°-α)+cosαcos(120°-α)化简
cos²α+cos²(120°-α)+cosαcos(120°-α)
cos²α+cos²(120°-α)+cosαcos(120°-α)化简cos²α+cos²(120°-α)+cosαcos(120°-α)
x=60°-α
则,通过积化和差与和差化积
原式化为
cos(x-60)^2+cos(x+60)^2+cos(x-60)cos(x+60)
=(cos(x-60)+cos(x+60))^2-cos(x-60)cos(x+60)
=cosx^2-cosx^2*(1/4)+sinx^2*(3/4)
=3/4