First slide

Properties of ITF

Question

$\sin^{- 1} (a - \frac{a^{2}}{3} + \frac{a^{3}}{9} + ....) + \cos^{- 1} (1 + b + b^{2} + .. .) = \frac{π}{2}$ then

Moderate

A

$a = - 3 and b = 1$
B

$a = 1 and b = - \frac{1}{3}$
C

$a = \frac{1}{6} and b = \frac{1}{2}$
D

None of these

Solution

The given relation is possible when $a - \frac{a^{2}}{3} + \frac{a^{3}}{9} + .... = 1 + b + b^{2} + ...$
Also $- 1 \leq a - \frac{a^{2}}{3} + \frac{a^{3}}{9} + ... \leq 1 and - 1 \leq 1 + b + b^{2} + ... \leq 1$
$\begin{array}{l} \Rightarrow | b | < 1 \Rightarrow | a | < 3 and \frac{a}{1 + \frac{a}{3}} = \frac{1}{1 - b} \\ \Rightarrow \frac{3 a}{a + 3} = \frac{1}{1 - b} \end{array}$

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