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1-sin60* = tan60*-1

Given: 1-sin60* = tan60*-1

To do: Prove LHS =RHS

Solution:

Let us simplify LEFT HAND SIDE:

= $\frac{1 -sin60°}{cos60°}$

= $\frac{1 - \frac{\sqrt{3}}{2}}{\frac{1}{2}}$

= $(2-\sqrt{3})$

Let us simplify Right HAND SIDE

= $\frac{ tan60° -1}{tan60° +1}$

=$\frac{\sqrt{3} -1}{\sqrt{3} +1}$

=$\frac{(\sqrt{3} -1)(\sqrt{3} -1)}{(\sqrt{3} +1)(\sqrt{3} -1)}$

=$\frac{ \sqrt{3^2} +1^2 -2√3}{\sqrt{3^2}-1}$

=$\frac{ 4-2\sqrt{3}}{2}$

= $2 -\sqrt{3}$

Therefore, LHS = RHS

Tutorialspoint

Updated on: 10-Oct-2022

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