First slide

Properties of ITF

Question

The value of $\tan [\cos^{- 1} (- \frac{2}{7}) - \frac{π}{2}]$ is

Easy

A

$\frac{2}{3 \sqrt{5}}$
B

$\frac{2}{3}$
C

$\frac{1}{\sqrt{5}}$
D

$\frac{4}{\sqrt{5}}$

Solution

$\begin{array}{l} = \tan \{\cos^{- 1} (- \frac{2}{7}) - \frac{π}{2}\} \\ = \tan \{π - \cos^{- 1} (\frac{2}{7}) - \frac{π}{2}\} \end{array} \begin{array}{l} = \tan \{\frac{π}{2} - \cos^{- 1} (\frac{2}{7})\} = \tan \{\sin^{- 1} (\frac{2}{7})\} \\ = \tan \tan^{- 1} (\frac{2}{3 \sqrt{5}}) = \frac{2}{3 \sqrt{5}} \end{array}$

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