First slide

Properties of ITF

Question

The value of cos (2 cos^–1x + sin^–1x) at x = $\frac{1}{5}$ is

Easy

A

$\frac{2 \sqrt{6}}{5}$
B

- $\frac{2 \sqrt{6}}{5}$
C

$\frac{3 \sqrt{6}}{5}$
D

none of these

Solution

cos (2 cos^–1x + sin^–1x)
= cos (cos^–1x + cos^–1x + sin^–1x)
$\begin{array}{l} = \cos (\frac{π}{2} + \cos^{- 1} x) = - \sin (\cos^{- 1} x) \\ = - \sin (\sin^{- 1} \sqrt{1 - x^{2}}) = - \sqrt{1 - x^{2}} \\ = - \sqrt{1 - \frac{1}{25}} = - \frac{2 \sqrt{6}}{5} \end{array}$

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