A) \[\tan \,3A\]
B) \[2\,\,tan\,3A\]
C) \[3\text{ }tan\text{ }3A\]
D) None of these
Correct Answer: C
Solution :
The given expression \[=\tan A+\left[ \frac{\sqrt{3}+\tan A}{1-\sqrt{3}\tan A} \right]-\left[ \frac{\sqrt{3}-\tan A}{1+\sqrt{3}\tan A} \right]\] \[=\tan A+\left[ \frac{8\tan A}{1-3{{\tan }^{2}}A} \right]=\frac{9\tan A-3{{\tan }^{3}}3}{1-3{{\tan }^{2}}A}\] \[=3.\frac{(3\tan A-{{\tan }^{3}}A)}{1-3{{\tan }^{2}}A}=3\tan 3A\]
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