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NDA Math Indefinite Integrals

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For the next two (2) items that follow :

The integral

\int \frac{dx}{a\cos x + b\sin x}

is of the form

\frac{1}{r} \ln \left[ \tan \left( \frac{x+\alpha}{2} \right) \right]

[NDA I 2015]

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Question : 32 of 38

Marks: +1, -0

What is α equal to?

$\tan^{-1}\left(\frac{a}{b}\right)$
$\tan^{-1}\left(\frac{b}{a}\right)$
$\tan^{-1}\left(\frac{a+b}{a-b}\right)$
$\tan^{-1}\left(\frac{a-b}{a+b}\right)$

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