已知cos(x-6分之π)=-3分之根3,则cosx+cos(x-3分之π)=

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已知cos(x-6分之π)=-3分之根3,则cosx+cos(x-3分之π)=
已知cos(x-6分之π)=-3分之根3,则cosx+cos(x-3分之π)=

已知cos(x-6分之π)=-3分之根3,则cosx+cos(x-3分之π)=
cosθ+cosφ = 2 cos[(θ+φ)/2] cos[(θ-φ)/2]
cosx+cos(x-π/3)
=2 cos[(x+x-π/3)/2] cos[(x-x+π/3)/2]
=2 cos(x-π/6) cosπ/6
=2(-3分之根3)(2分之根3)
=-1

cosx+cos(x-π/3)
=2 cos[(x+x-π/3)/2] cos[(x-x+π/3)/2]
=2 cos(x-π/6) cosπ/6
=2(-3分之根3)(2分之根3)
=-1