Question : If $A=60^{\circ}$ and $B=30^{\circ}$, find the value of $\frac{(\tan A-\tan B)}{(1+\tan A \tan B)}$.
Option 1: $3$
Option 2: $\frac{1}{\sqrt{3}}$
Option 3: $\sqrt{3}$
Option 4: $1$
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Correct Answer: $\frac{1}{\sqrt{3}}$
Solution :
Given, $A=60^{\circ}$ and $B=30^{\circ}$
We know, $\frac{(\tan A-\tan B)}{(1+\tan A \tan B)}=\tan(A-B)=\tan(60^{\circ}-30^{\circ})=\tan30^{\circ}=\frac{1}{\sqrt3}$
Hence, the correct answer is $\frac{1}{\sqrt3}$.
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