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Question: If \(\tan A = \frac{1}{2},\) then \(\tan 3A =\)...

If tan⁡A=12,\tan A = \frac{1}{2}, then tan⁡3A=\tan 3A =

A

92\frac{9}{2}

B

112\frac{11}{2}

C

72\frac{7}{2}

D

−12- \frac{1}{2}

Answer

112\frac{11}{2}

Explanation

Solution

We have tan⁡A=12\tan A = \frac{1}{2}

⇒tan⁡3A=3tan⁡A−tan⁡3A1−tan⁡2A=3.12−181−3.14=12−12=112\Rightarrow \tan 3A = \frac{3\tan A - \tan^{3}A}{1 - \tan^{2}A} = \frac{3.\frac{1}{2} - \frac{1}{8}}{1 - 3.\frac{1}{4}} = \frac{12 - 1}{2} = \frac{11}{2}.