First slide

Properties of ITF

Question

If $\sec^{- 1} x = {cosec}^{- 1} y,$ then $\cos^{- 1} \frac{1}{x} + \cos^{- 1} \frac{1}{y} =$

Moderate

A

$π$
B

$\frac{π}{4}$
C

$- \frac{π}{2}$
D

$\frac{π}{2}$

Solution

We have,
$\sec^{- 1} x = {cosec}^{- 1} y \Rightarrow \cos^{- 1} \frac{1}{x} = \sin^{- 1} \frac{1}{y}$
$∴ \cos^{- 1} \frac{1}{x} + \cos^{- 1} \frac{1}{y} = \sin^{- 1} \frac{1}{y} + \cos^{- 1} \frac{1}{y} = \frac{π}{2}$

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