First slide

Properties of ITF

Question

If $4 \sin^{- 1} x + \cos^{- 1} x = π$ then $x$ equal

Moderate

A

$\frac{1}{2}$
B

$\frac{\sqrt{3}}{2}$
C

$- \frac{1}{2}$
D

none of these

Solution

We have,
$\begin{array}{l} 4 \sin^{- 1} x + \cos^{- 1} x = π \\ \Rightarrow 4 \sin^{- 1} x + \frac{π}{2} - \sin^{- 1} x = π \\ \Rightarrow 3 \sin^{- 1} x = \frac{π}{2} \Rightarrow x = \sin (\frac{π}{6}) = \frac{1}{2} \end{array}$

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