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Q.

Two angles of a triangle are ${Cot}^{- 1} 2 and {Cot}^{- 1} 3$ Then the third angle is

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a

π/4

b

π/3

c

π/6

d

3π/4

answer is B.

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Detailed Solution

Third angle $= π - ({Cot}^{- 1} 2 + {Cot}^{- 1} 3) = π - [{Tan}^{- 1} \frac{1}{2} + {Tan}^{- 1} \frac{1}{3}] = π - [{Tan}^{- 1} \frac{1 / 2 + 1 / 3}{1 - 1 / 2 \cdot 1 / 3}]$
$= π - {Tan}^{- 1} (\frac{5}{5}) = π - \frac{π}{4} = \frac{3 π}{4}$

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