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  • If tan⁡A=1/2 tan⁡B=1/3then tan (2A + B) is equal to A. 1 B. 2 C. 3 D. 4

If \tan A=\frac{1}{2} , \tan B=\frac{1}{3} \\\\  then \tan (2A + B)  is equal to

A. 1

B. 2

C. 3

D. 4

Answers (1)

The answer is the option (c). 

\\ \tan A=\frac{1}{2} \\\\ \tan B=\frac{1}{3} \\\\ \tan 2A=\frac{2\tan A}{1 - \tan ^{2}A}=\frac{4}{3} \\\\ \tan \left( 2A+B \right) =\frac{\tan 2A+\tan B}{1 - \tan 2A\tan B} \\\\ =\frac{\frac{4}{3}+\frac{1}{3}}{1 - \frac{4}{3} \times \frac{1}{3}}= \left( \frac{5}{3} \right) \times \left( \frac{9}{5} \right) =3 \\\\

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infoexpert21

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