First slide

Properties of ITF

Question

$\tan [\tan^{- 1} (\frac{1}{a + b}) + \tan^{- 1} (\frac{b}{a^{2} + a b + 1})] =$

Moderate

A

$a$
B

$\frac{1}{a}$
C

$b$
D

$\frac{1}{b}$

Solution

$w e h a v e \tan [\tan^{- 1} (\frac{1}{a + b}) + \tan^{- 1} (\frac{b}{a^{2} + a b + 1})] = \tan [\tan^{- 1} (\frac{1}{a + b}) + \tan^{- 1} (\frac{(a + b) - a}{1 + (a + b) a})] = \tan [\tan^{- 1} (\frac{1}{a + b}) + \tan^{- 1} (a + b) - \tan^{- 1} a] = \tan (\frac{π}{2} - \tan^{- 1} a) = \tan (c o t^{- 1} a) = \tan (\tan^{- 1} \frac{1}{a}) = \frac{1}{a}$

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