显示
1-sin60* = tan60*-1
给定: 1-sin60* = tan60*-1
待做:证明 LHS =RHS
解
让我们化简 LEFT HAND SIDE
= \frac{1 -sin60°}{cos60°}
= \frac{1 - \frac{\sqrt{3}}{2}}{\frac{1}{2}}
= (2-\sqrt{3})
让我们化简 RIGHT HAND SIDE
= \frac{ tan60° -1}{tan60° +1}
=\frac{\sqrt{3} -1}{\sqrt{3} +1}
=\frac{(\sqrt{3} -1)(\sqrt{3} -1)}{(\sqrt{3} +1)(\sqrt{3} -1)}
=\frac{ \sqrt{3^2} +1^2 -2√3}{\sqrt{3^2}-1}
=\frac{ 4-2\sqrt{3}}{2}
= 2 -\sqrt{3}
因此,LHS = RHS
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