First slide

Properties of ITF

Question

$\cos^{- 1} \sqrt{\frac{a - x}{a - b}} = \sin^{- 1} \sqrt{\frac{x - b}{a - b}} (a \neq b)$ is possible if

Moderate

A

$a \geq x \geq b$ or $a \leq x \leq b$
B

$a = x = b$
C

$a > b$ And x takes any value
D

$a < b$ And x takes any value

Solution

Take $\sqrt{\frac{a - x}{a - b}} = \sqrt{\frac{x - b}{a - b}} = \frac{1}{\sqrt{2}}$
$T h e n \frac{a - x}{a - b} = \frac{1}{2} \Rightarrow 2 a - 2 x = a - b \Rightarrow x = \frac{a + b}{2} \Rightarrow a \leq x ⩽ b o r a \geq x \geq b$

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