First slide

Properties of ITF

Question

$\sin^{- 1} (\frac{3}{5}) + \tan^{- 1} (\frac{1}{7}) =$

Moderate

A

$\frac{π}{4}$
B

$\frac{π}{2}$
C

$\cos^{- 1} (\frac{4}{5})$
D

$π$

Solution

We have,
$\begin{array}{l} \sin^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{7} \\ = \tan^{- 1} \frac{3}{4} + \tan^{- 1} \frac{1}{7} \\ = \tan^{- 1} \{\frac{3 / 4 + 1 / 7}{1 - 3 / 4 \times 1 / 7}\} = \tan^{- 1} (\frac{25}{25}) = \tan^{- 1} 1 = \frac{π}{4} \end{array}$

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