求证:[tan(2π-α)cos(3π/2-α)cos(6π-α)]/[sin(α+3π/2)cos(α+3π/2)]=-tanα

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求证:[tan(2π-α)cos(3π/2-α)cos(6π-α)]/[sin(α+3π/2)cos(α+3π/2)]=-tanα

求证:[tan(2π-α)cos(3π/2-α)cos(6π-α)]/[sin(α+3π/2)cos(α+3π/2)]=-tanα
求证:[tan(2π-α)cos(3π/2-α)cos(6π-α)]/[sin(α+3π/2)cos(α+3π/2)]=-tanα

求证:[tan(2π-α)cos(3π/2-α)cos(6π-α)]/[sin(α+3π/2)cos(α+3π/2)]=-tanα
全用诱导公式处理:

tan(2π-α)=tan(-α)=-tanα
sin(-3π/2-α)=sin(-α)=-sinα
cos(6π-α)=cos(-α)=cosα
sin(α+3π/2)=-cosα
cos(α+3π/2)=sinα
∴原式=(-tanα)(-sinα)cosα/[(-cosα)sinα]=-tanα

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