∫ (1)/(2 + cos x)dx equals A. 1/3 tan^(-1)(1/√3) B. 2/√3 tan^(-1)(1/√3) C. √3tan^(-1)(√3) D. 2√3 tan^(-1)√3

Question

\(\int\limits_{0}^{\pi/2}\cfrac{1}{2+cos\,\text x}d\text x\) equals

A. \(\cfrac13tan^{-1}(\cfrac{1}{\sqrt3})\)

B. \(\cfrac2{\sqrt3}tan^{-1}(\cfrac{1}{\sqrt3})\)

C. \({\sqrt3}tan^{-1}(\sqrt3)\)

D. \({2\sqrt3}tan^{-1}\sqrt3\)

Answer 1

Correct option is  B. \(\cfrac2{\sqrt3}tan^{-1}(\cfrac{1}{\sqrt3})\) 

Let, tan \(\cfrac{x}2\) = t

Differentiating both side with respect to x