Let \( \alpha \) and \( \beta \) be non-zero real numbers such that \( 2(\cos \beta-\cos \alpha)...
Let \( \alpha \) and \( \beta \) be non-zero real numbers such that \( 2(\cos \beta-\cos \alpha)+\cos \alpha \cos \beta=1 \). Then which of the following is/are true?
(a) \( \tan \left(\frac{\alpha}{2}\right)+\sqrt{3} \tan \left(\frac{\beta}{2}\right)=0 \)
(b) \( \sqrt{3} \tan \left(\frac{\alpha}{2}\right)+\tan \left(\frac{\beta}{2}\right)=0 \)
(c) \( \tan \left(\frac{\alpha}{2}\right)-\sqrt{3} \tan \left(\frac{\beta}{2}\right)=0 \)
(d) \( \sqrt{3} \tan \left(\frac{\alpha}{2}\right)-\tan \left(\frac{\beta}{2}\right)=0 \)
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