First slide

Introduction to ITF

Question

$If θ = \sin^{- 1} x + \cos^{- 1} x - \tan^{- 1} x \geq 0,$ then the smallest interval in which $θ$ lies, is given by

NA

A

$\frac{π}{2} \leq θ \leq \frac{3 π}{4}$
B

$- \frac{π}{4} \leq θ \leq 0$
C

$0 \leq θ \leq \frac{π}{4}$
D

$\frac{π}{4} \leq θ \leq \frac{π}{2}$

Solution

We have, $θ = \sin^{- 1} x + \cos^{- 1} x - \tan^{- 1} x$
$= \frac{π}{2} - \tan^{- 1} x = \cot^{- 1} x$
$Since, 0 \leq x \leq 1, therefore \frac{π}{4} \leq θ \leq \frac{π}{2}$

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