First slide

Properties of ITF

Question

If $a > b > c > 0$ then $\cot^{- 1} (\frac{a b + 1}{a - b}) + \cot^{- 1} (\frac{b c + 1}{b - c}) + \cot^{- 1} (\frac{c a + 1}{c - a}) =$

Moderate

A

0
B

$\frac{π}{2}$
C

$π$
D

$\frac{3 π}{2}$

Solution

$S i n c e a > b > c > 0, w e h a v e a - b > 0, b - c > 0 a n d c - a < 0 ∴ \cot^{- 1} (\frac{a b + 1}{a - b}) + \cot^{- 1} (\frac{b c + 1}{b - c}) + \cot^{- 1} (\frac{c a + 1}{c - a}) = \cot^{- 1} (\frac{a b + 1}{a - b}) + \cot^{- 1} (\frac{b c + 1}{b - c}) + \cot^{- 1} (- \frac{c a + 1}{a - c}) = c o t^{- 1} (a) - c o t^{- 1} (b) + c o t^{- 1} (b) - c o t^{- 1} c + π - [\cot^{- 1} (a) - \cot^{- 1} c] (∵ \cot^{- 1} (- x) = π - \cot^{- 1} (x)) = π$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App