First slide

Introduction to ITF

Question

Statement : 1) $C o \sec e^{- 1} (\frac{1}{2} + \frac{1}{\sqrt{2}}) > S e c^{- 1} (\frac{1}{2} + \frac{1}{\sqrt{2}})$
Statement : 2) $C o \sec^{- 1} x < S e c^{- 1} x$ if $1 \leq x < \sqrt{2}$

Moderate

A

Both 1,2 are true , and 2 is the correct explanation of 1.
B

Both 1 and 2 are true but 2 is not the correct explanation of 2.
C

1 is true but 2 is false.
D

1 is false but 2 is true

Solution

$\begin{array}{l} I f {Cosec}^{- 1} x > {Sec}^{- 1} x \\ \Rightarrow {Cosec}^{- 1} x > \frac{π}{2} - {Cosec}^{- 1} x \\ \Rightarrow Co \sec^{- 1} x > \frac{π}{4} \\ \Rightarrow 1 \leq x < \sqrt{2} and (\frac{1}{2} + \frac{1}{\sqrt{2}}) \in [1, \sqrt{2}] \end{array}$
$∴ S t a t e m e n t (1) i s t r u e a n d s t a t e m e n t (2) i s f a l s e .$

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