大师作文网(3)sin29π/9cos4π/9+sin41π/18cos19π/18
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(3)sin29π/9cos4π/9+sin41π/18cos19π/18
sin29π/9cos4π/9+sin41π/18cos19π/18
=sin(4π-7π/9)cos4π/9+sin(2π+5π/18)cos(π+π/18)
=-sin7π/9cos4π/9-sin5π/18cosπ/18
=-sin2π/9cos4π/9-sin5π/18cosπ/18
sinαcosβ=1/2[sin(α+β)+sin(α-β)]
上式=-1/2[sin(2π/9+4π/9)+sin(2π/9-4π/9)]-1/2[sin(5π/18+π/18)+sin(5π/18-π/18)]
=-1/2[sin2π/3 +sin(-2π/9)]-1/2[sinπ/3+sin(2π/9)]
=-1/2[sinπ/3 -sin(2π/9)+sinπ/3+sin(2π/9)]
=-1/2[2sinπ/3 ]
=-√3/2
=sin(4π-7π/9)cos4π/9+sin(2π+5π/18)cos(π+π/18)
=-sin7π/9cos4π/9-sin5π/18cosπ/18
=-sin2π/9cos4π/9-sin5π/18cosπ/18
sinαcosβ=1/2[sin(α+β)+sin(α-β)]
上式=-1/2[sin(2π/9+4π/9)+sin(2π/9-4π/9)]-1/2[sin(5π/18+π/18)+sin(5π/18-π/18)]
=-1/2[sin2π/3 +sin(-2π/9)]-1/2[sinπ/3+sin(2π/9)]
=-1/2[sinπ/3 -sin(2π/9)+sinπ/3+sin(2π/9)]
=-1/2[2sinπ/3 ]
=-√3/2
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