First slide

Introduction to ITF

Question

The number of solutions of the equation $2 {(\sin^{- 1} x)}^{2} - 5 \sin^{- 1} x + 2 = 0$ is

Easy

A

0
B

1
C

2
D

3

Solution

$W e h a v e 2 {(\sin^{- 1} x)}^{2} - 5 \sin^{- 1} x + 2 = 0 \Rightarrow (2 \sin^{- 1} x - 1) (\sin^{- 1} x - 2) = 0 \Rightarrow 2 \sin^{- 1} x - 1 = 0 (∵ - \frac{π}{2} \leq \sin^{- 1} x \leq \frac{π}{2} \Rightarrow \sin^{- 1} x - 2 \neq 0) \Rightarrow x = \sin (\frac{1}{2}) i s t h e o n l y s o l u t i o n o f t h e e q u a t i o n$

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