First slide

Properties of ITF

Question

$T a n^{- 1} (\frac{p}{q}) + T a n^{- 1} (\frac{q - p}{q + p}) =$

Moderate

A

$\frac{π}{4}$
B

$\frac{π}{2}$
C

$\frac{3 π}{4}$
D

$\frac{- π}{4}$

Solution

$W e h a v e, \tan^{- 1} (\frac{p}{q}) + \tan^{- 1} (\frac{q - p}{q + p}) = \tan^{- 1} (\frac{p}{q}) + \tan^{- 1} (\frac{1 - \frac{p}{q}}{1 + \frac{p}{q}}) (\sin c e \tan^{- 1} (\frac{x - y}{1 + x y}) = \tan^{- 1} x - \tan^{- 1} y) = \tan^{- 1} (\frac{p}{q}) + t {an}^{- 1} (1) - t {an}^{- 1} (\frac{p}{q}) = \frac{π}{4}$

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