There exist \theta such that a>|\sec \theta|, then \int \frac{d x}{1+a \cos x}=

Correct Answer is : 1√a2−1log(√a+1cosx2+√a−1sinx2√a+1cosx2−√a−1sinx2)+C

{1}/\sqrt{a^{2}-1}} \tan ^{-1}( \sqrt{a-1}/\sqrt{a+1} \tan \frac{x}{2})+C

{1}/\sqrt{a^{2}-1}} \tan ^{-1}(\sqrt{\frac{1-a}{1+a}} \tan \frac{x}{2})+C

{1}/\sqrt{a^{2}-1}} \log ( \sqrt{a+1} \cos \frac{x}{2}-\sqrt{a-1} \sin \frac{x}{2}}/\sqrt{a-1} \cos \frac{x}{2}+\sqrt{a-1} \sin \frac{x}{2}})+C

{1}/\sqrt{a^{2}-1}} \log ( \sqrt{a+1} \cos \frac{x}{2}+\sqrt{a-1} \sin \frac{x}{2}}/\sqrt{a+1} \cos \frac{x}{2}-\sqrt{a-1} \sin \frac{x}{2}})+C

AP EAPCET 05-Jul-2022 Shift 2 Paper

Section: Mathematics

Question : 70 of 160

Marks: +1, -0

There exist θ such that a>|sec‌θ|, then ∫‌

1+a‌cos‌x

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