Question : What is the value of $\frac{\tan 45^{\circ}-\tan 15^{\circ}}{1+\tan 45^{\circ} \tan 15^{\circ}}$?
Option 1: $\sqrt{3}$
Option 2: $\frac{1}{\sqrt{2}}$
Option 3: $\frac{1}{\sqrt{3}}$
Option 4: ${\sqrt{2}}$
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Correct Answer: $\frac{1}{\sqrt{3}}$
Solution :
$\frac{\tan 45^{\circ}-\tan 15^{\circ}}{1+\tan 45^{\circ} \tan 15^{\circ}}$
$= \tan (45^{\circ}-15^{\circ})$
$=\tan 30^{\circ}$
$= \frac{1}{\sqrt3}$
Hence, the correct answer is $\frac{1}{\sqrt3}$.
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