If \tan \A = 1 /2 and \tan \B = 1 /3, then what is the value of \tan(2\A + \B)?

SSC CGL Model Paper 12

Question : 71 of 100

Marks: +1, -0

\tan \A = 1 /2

and

\tan \B = 1 /3

, then what is the value of

\tan(2\A + \B)

Solution:

\tan \A = 1 /2

and

\tan \B = 1 /3

\tan 2\A={2\tan \A}/{1-\tan^2\A}

={2×1/2}/{1-1/4}=4/3

\tan(2\A+\B)={\tan 2\A+\tan \B}/{1-\tan 2\A\tan \B}

={4/3+1/3}/{1-4/3×1/3}

=5/3×9/5=3

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