prove that `2tan^-1(sqrt((a-b)/(a+b))tan(theta/2))`=`cos^-1((acostheta+b)/(a+bcostheta))`

Explanation

To prove that

\[ 2\tan^{-1}\left(\sqrt{\frac{a-b}{a+b}} \tan\left(\frac{\theta}{2}\right)\right) = \cos^{-1}\left(\frac{a\cos\theta + b}{a + b\cos\theta}\right), \]

we will start with the left-hand side (LHS) and manipulate it to show that it equals the right-hand side (RHS).

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