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Problem Let α \alpha α β \beta β 2 ( cos β − cos α ) + cos α cos β = 1 2(\cos \beta - \cos \alpha) + \cos \alpha \cos \beta = 1 2 ( cos β − cos α ) + cos α cos β = 1 3 tan ( α 2 ) − tan ( β 2 ) = 0 \sqrt{3} \tan\left(\frac{\alpha}{2}\right) - \tan\left(\frac{\beta}{2}\right) = 0 3 tan ( 2 α ) − tan ( 2 β ) = 0 tan ( α 2 ) − 3 tan ( β 2 ) = 0 \tan\left(\frac{\alpha}{2}\right) - \sqrt{3} \tan\left(\frac{\beta}{2}\right) = 0 tan ( 2 α ) − 3 tan ( 2 β ) = 0 tan ( α 2 ) + 3 tan ( β 2 ) = 0 \tan\left(\frac{\alpha}{2}\right) + \sqrt{3} \tan\left(\frac{\beta}{2}\right) = 0 tan ( 2 α ) + 3 tan ( 2 β ) = 0 3 tan ( α 2 ) + tan ( β 2 ) = 0 \sqrt{3} \tan\left(\frac{\alpha}{2}\right) + \tan\left(\frac{\beta}{2}\right) = 0 3 tan ( 2 α ) + tan ( 2 β ) = 0 Browse the problem library