JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Trigonometrical ratios of multiple and sub multiple angles

  • question_answer
    If \[\tan \beta =\cos \theta \tan \alpha ,\]then \[{{\tan }^{2}}\frac{\theta }{2}=\]

    A) \[\frac{\sin (\alpha +\beta )}{\sin (\alpha -\beta )}\]

    B) \[\frac{\cos (\alpha -\beta )}{\cos (\alpha +\beta )}\]

    C) \[\frac{\sin (\alpha -\beta )}{\sin (\alpha +\beta )}\]

    D) \[\frac{\cos (\alpha +\beta )}{\cos (\alpha -\beta )}\]

    Correct Answer: C

    Solution :

    \[{{\tan }^{2}}\frac{\theta }{2}=\frac{1-\cos \theta }{1+\cos \theta }=\frac{\tan \alpha -\tan \beta }{\tan \alpha +\tan \beta }=\frac{\sin (\alpha -\beta )}{\sin (\alpha +\beta )}\].


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