First slide

Properties of ITF

Question

If $a \sin^{- 1} x - b \cos^{- 1} x = c$ then the value of $a \sin^{- 1} x + b \cos^{- 1} x =$

Moderate

A

0
B

$\frac{π}{2}$
C

$\frac{π a b + c (b - a)}{a + b}$
D

$\frac{π a b + c (a - b)}{a + b}$

Solution

$G i v e n$ $a \sin^{- 1} x - b \cos^{- 1} x = c \to (1)$
$W e k n o w t h a t$ $a \sin^{- 1} x + a \cos^{- 1} x = a \frac{π}{2} \to (2)$
$A l s o b \sin^{- 1} x + b \cos^{- 1} x = b \frac{π}{2} \to (3)$
$N o w e q u a t i o i n s (2) - (1) \Rightarrow$ $C o s^{- 1} x = \frac{\frac{a π}{2} - c}{a + b}$
$a n d e q u a t i o n s (3) + (1) \Rightarrow \sin^{- 1} x = \frac{b \frac{π}{2} + c}{a + b}$
$∴ a \sin^{- 1} x + b \cos^{- 1} x = \frac{π a b + c (a - b)}{a + b}$

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