First slide

Properties of ITF

Question

$If \tan^{- 1} \frac{a}{x} + \tan^{- 1} \frac{b}{x} = \frac{π}{2}, then x =$

Moderate

A

$\sqrt{a b}$
B

$\sqrt{2 a b}$
C

$2 a b$
D

$a b$

Solution

We have,
$\begin{array}{l} \tan^{- 1} \frac{a}{x} + \tan^{- 1} \frac{b}{x} = \frac{π}{2} \\ \Rightarrow \tan^{- 1} (\frac{\frac{a}{x} + \frac{b}{x}}{1 - \frac{a b}{x^{2}}}) = \frac{π}{2} \Rightarrow 1 - \frac{a b}{x^{2}} = 0 \Rightarrow x = \sqrt{a b} \end{array}$

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