First slide

Properties of ITF

Question

The Value of $\cos^{- 1} \sqrt{\frac{2}{3}} - \cos^{- 1} \frac{\sqrt{6} + 1}{2 \sqrt{3}}$ is equal to

Moderate

A

$\frac{π}{3}$
B

$\frac{π}{4}$
C

$\frac{π}{2}$
D

$\frac{π}{6}$

Solution

$\cos^{- 1} \sqrt{\frac{2}{3}} - \cos^{- 1} \frac{\sqrt{6} + 1}{2 \sqrt{3}}$
$\begin{array}{l} = \tan^{- 1} (\frac{1}{\sqrt{2}}) - \tan^{- 1} (\frac{\sqrt{3} - \sqrt{2}}{1 + \sqrt{6}}) \\ = \tan^{- 1} (\frac{\frac{1}{\sqrt{2}} - \frac{\sqrt{3} - \sqrt{2}}{1 + \sqrt{6}}}{1 + \frac{\sqrt{3} - \sqrt{2}}{\sqrt{2} (1 + \sqrt{6})}}) = \tan^{- 1} (\frac{1}{\sqrt{3}}) = \frac{π}{6} \end{array}$

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