First slide

Properties of ITF

Question

$\cos^{- 1} (\frac{15}{17}) + 2 \tan^{- 1} (\frac{1}{5}) =$

Moderate

A

$\frac{π}{2}$
B

$\cos^{- 1} (\frac{171}{221})$
C

$\frac{π}{4}$
D

$\cos^{- 1} (\frac{140}{221})$

Solution

We have,
$\begin{array}{l} \cos^{- 1} (\frac{15}{17}) + 2 \tan^{- 1} (\frac{1}{5}) \\ = \cos^{- 1} (\frac{15}{17}) + \cos^{- 1} (\frac{1 - 1 / 25}{1 + 1 / 25}) \\ = \cos^{- 1} (\frac{15}{17}) + \cos^{- 1} (\frac{12}{13}) \end{array}$
$= \cos - 1 \{\frac{15}{17} \times \frac{12}{13} - \sqrt{1 - {(\frac{15}{17})}^{2}} \sqrt{1 - {(\frac{12}{13})}^{2}}\} = \cos^{- 1} (\frac{140}{221})$

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