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Question: If tan \(\left( \tan ^ { - 1 } \frac { 1 } { 2 } + \tan ^ { - 1 } \frac { 1 } { 3 } + \tan ^ { - 1 }...

If tan (tan⁡−112+tan⁡−113+tan⁡−114+tan⁡−115)\left( \tan ^ { - 1 } \frac { 1 } { 2 } + \tan ^ { - 1 } \frac { 1 } { 3 } + \tan ^ { - 1 } \frac { 1 } { 4 } + \tan ^ { - 1 } \frac { 1 } { 5 } \right)= then a + b

equals (a & b are in their lowest form)

A

27

B

19

C

38

D

None of these

Answer

19

Explanation

Solution

Using tan–1x + tan–1y = tan–1(x+y1−xy)\left( \frac { x + y } { 1 - x y } \right)