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Question: 2 tan<sup>–1</sup>\(\frac{1}{3}\)+ tan<sup>–1</sup>\(\frac{1}{2}\)=...

2 tan–113\frac{1}{3}+ tan–112\frac{1}{2}=

A

900

B

600

C

450

D

tan–1 2

Answer

tan–1 2

Explanation

Solution

2 tan–113\frac{1}{3}+ tan–112\frac{1}{2}

= tan–1 [2(1/3)1−1/9]\left\lbrack \frac{2(1/3)}{1 - 1/9} \right\rbrack+ tan–112\frac{1}{2}

= tan–1 [34]\left\lbrack \frac{3}{4} \right\rbrack+ tan–112\frac{1}{2}

= tan–1 [3/4+1/21−(3/4).(1/2)]\left\lbrack \frac{3/4 + 1/2}{1 - (3/4).(1/2)} \right\rbrack= tan–1 (2)