First slide

Properties of ITF

Question

sin^–1 [cos (sin^–1x)] + cos^–1 [sin (cos^–1x)] is equal to

Moderate

A

$\frac{π}{4}$
B

$\frac{π}{2}$
C

$\frac{3 π}{4}$
D

0

Solution

We have
sin^–1cos (sin^–1x)) + cos^–1(sin (cos^–1x))
$\begin{array}{l} = \sin^{- 1} [\cos (\frac{π}{2} - \cos^{- 1} x)] + \cos^{- 1} [\sin (\frac{π}{2} - \sin^{- 1} x)] \\ = \sin^{- 1} [\sin (\cos^{- 1} x)] + \cos^{- 1} [\cos (\sin^{- 1} x)] \\ = \cos^{- 1} x + \sin^{- 1} x = \frac{π}{2} \end{array}$

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