First slide

Properties of ITF

Question

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

Easy

A

1
B

0
C

4/5
D

1/5

Solution

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

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