First slide

Properties of ITF

Question

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

Moderate

A

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

$\frac{2}{3}$
C

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

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

Solution

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

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