Answer :
The value of the given expression is 1 / √3.
What is trigonometry?
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
The given values are cos60=sin30=1/2 and cos30=sin60=√3/2.
Divide sin30 and cos30,
[tex]\dfrac{sin30}{cos30}=tan30 = \dfrac{\dfrac{1}{2}}{\dfrac{2}{\sqrt{3}}}=\dfrac{1}{\sqrt{3}}[/tex]
Divide sin60 and cos60.
[tex]\dfrac{sin60}{cos60}=tan60 = \dfrac{\dfrac{2}{\sqrt{3}}}{\dfrac{1}{2}}= \sqrt3[/tex]
The value of the expression is.
[tex]\dfrac{ tan60-1}{1-tan30}=\dfrac{\sqrt{3}-1}{\sqrt{3}-1}}\times \dfrac{1}{\sqrt{3}}=\dfrac{1}{\sqrt{3}}[/tex]
Therefore, the value of the given expression is 1 / √3.
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