First slide

Properties of ITF

Question

If (a < 0) and x ∈ (– a, a), then $\tan^{- 1} (\frac{x}{\sqrt{a^{2} - x^{2}}}) =$

Easy

A

$- \sin^{- 1} (\frac{x}{a})$
B

$\sin^{- 1} (\frac{x}{a})$
C

$\cos^{- 1} (\frac{x}{a})$
D

none of these

Solution

Put x = a sin θ, then the given expression
$\begin{array}{l} = \tan^{- 1} (\frac{asin θ}{- acos θ}) (∵ a < 0) \\ = \tan^{- 1} (- \tan θ) = - θ = - \sin^{- 1} \frac{x}{a} \end{array}$

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