sinα^2+sin(120°-α)^2怎么化简

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sinα^2+sin(120°-α)^2怎么化简sinα^2+sin(120°-α)^2怎么化简sinα^2+sin(120°-α)^2怎么化简sinα^2+sin(120°-α)^2=sinα^2+

sinα^2+sin(120°-α)^2怎么化简
sinα^2+sin(120°-α)^2怎么化简

sinα^2+sin(120°-α)^2怎么化简
sinα^2+sin(120°-α)^2=sinα^2+sin(60°+α)^2=sinα^2+[sin60cosα+cos60sinα]^2
=sinα^2+(3/4cosα^2+1/4sinα^2+2*sin60*cos60*sinα*cosα)
=1/2sinα^2+(3/4cosα^2+3/4sinα^2)+sin60sinαcosα
=1/4(1-cos2α)+1+1/2sin60sin2α
=5/4+1/2(sin60sin2α-1/2cos2α)
=5/4-1/2cos(2α+60)