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
\(\frac{1}{2}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{tan 60^o - tan 30^o}{tan 60^o + tan 30^o}= \frac{\sqrt{3}-\frac{1}{\sqrt{3}}}{\sqrt{3}+\frac{1}{\sqrt{3}}}\\
=\left(\frac{\sqrt{3}\sqrt{3}-1}{\sqrt{3}}\right)\div \left(\frac{\sqrt{3}\sqrt{3}+1}{\sqrt{3}}\right)\\
=\frac{(3-1)}{(3+1)}\\
=\frac{2}{4}=\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #9255)