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Find the value of frac tan 60 o - tan 30 o tan ... - JAMB Mathematics 2007 Question

Find the value of \(\frac{tan 60^o - tan 30^o}{tan 60^o + tan 30^o}\)
A
\(\frac{4}{\sqrt{3}}\)
B
\(\frac{2}{\sqrt{3}}\)
C
1
D
\(\frac{1}{2}\)
correct option: d

(\frac{tan 60^o - tan 30^o}{tan 60^o + tan 30^o}= \frac{\sqrt{3}-\frac{1}{\sqrt{3}}}{\sqrt{3}+\frac{1}{\sqrt{3}}}\

=\left(\frac{\sqrt{3}\sqrt{3}-1}{\sqrt{3}}\right)\div \left(\frac{\sqrt{3}\sqrt{3}+1}{\sqrt{3}}\right)\

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

=\frac{2}{4}=\frac{1}{2})

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