cos(α+5π/12)cos(α+π/6)+cos(π/12-α)cos(π/3-α) 化简 求化简过程~！ 在线等
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cos(α+5π/12)cos(α+π/6)+cos(π/12-α)cos(π/3-α)
=cos(α+5π/12)cos(α+π/6)+cos[π/2-(5π/12+α)]cos[π/2-(π/6+α)]
=cos(α+5π/12)cos(α+π/6)+sin(5π/12+α)sin(π/6+α)
=cos[(α+5π/12)-(α+π/6)]
=cos(5π/12-π/6)
=cos(π/4)
=√2/2
=cos(α+5π/12)cos(α+π/6)+cos[π/2-(5π/12+α)]cos[π/2-(π/6+α)]
=cos(α+5π/12)cos(α+π/6)+sin(5π/12+α)sin(π/6+α)
=cos[(α+5π/12)-(α+π/6)]
=cos(5π/12-π/6)
=cos(π/4)
=√2/2
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