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NDA Math Indefinite Integrals

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]

Question : 32 of 38

Marks: +1, -0

What is α equal to?

Solution:

From the solution of the above question, the constant angle can written as

\sin\alpha = \frac{a}{\sqrt{a^2+b^2}}

\cos\alpha = \frac{b}{\sqrt{a^2+b^2}}

\tan\alpha = \frac{a}{b}

\alpha = \tan^{-1}\left(\frac{a}{b}\right)

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