First slide

Properties of ITF

Question

The value of $\cos (2 \cos^{- 1} 0.8)$ , is

Moderate

A

$0.48$
B

$0.96$
C

$0.6$
D

$0.28$

Solution

We have,
$\begin{array}{l} 2 \cos^{- 1} x = \cos^{- 1} (2 x^{2} - 1) \\ \Rightarrow 2 \cos^{- 1} 0.8 = \cos^{- 1} (2 \times 0.64 - 1) = \cos^{- 1} (0.28) \\ \Rightarrow \cos (2 \cos^{- 1} 0.8) = \cos (\cos^{- 1} 0.28) = 0.28 \end{array}$

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