Q:

Evaluate the following integral∫1/(2+cos⁡x ) dx

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Evaluate the following integral∫1/(2+cos⁡x  )  dx

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Put  z=tan⁡〖x/2〗     ,    cos⁡x=(1-z^2)/(1+z^2 )     and    dz=2dz/(1+z^2 )
I=∫dz/(2+(1-z^2)/(1+z^2 ))=∫2dz/(1+z^2 )=2/√3  tan^(-1)⁡(z/√3)+c
I=2/√3  tan^(-1)⁡(tan⁡〖x/2〗/√3)+c

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