First slide

Properties of ITF

Question

If $\sin (\sin^{- 1} \frac{1}{5} + \cos^{- 1} x) = 1,$ then $x$ is equal to

Moderate

A

1
B

0
C

$4 / 5$
D

$1 / 5$

Solution

We have,
$\sin (\sin^{- 1} 1 / 5 + \cos^{- 1} x) = 1$
$\begin{array}{l} \Rightarrow \sin^{- 1} \frac{1}{5} + \cos^{- 1} x = \frac{π}{2} \\ \Rightarrow \sin^{- 1} \frac{1}{5} = \frac{π}{2} - \cos^{- 1} x \Rightarrow \sin^{- 1} \frac{1}{5} = \sin^{- 1} x \Rightarrow x = \frac{1}{5} \end{array}$

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