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Prove that : cos^(-1)((cosalpha+cosbeta)...

Prove that : `cos^(-1)((cosalpha+cosbeta)/(1+cosalphacosbeta))=2\ tan^(-1)(tan(alpha/2)tan(beta/2))`

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`\cos ^{-1}[\frac{\cos \alpha+\cos \beta}{1+\cos \alpha \cos \beta}]=2 \tan ^{-1}(\tan \frac{\alpha}{2} \tan \frac{\beta}{2})`
RHS
`=2 \tan^{-1}[\tan \frac{\alpha}{2} \tan \frac{\beta}{2}]`
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