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

  • question_answer
    If \[\tan \alpha =\frac{1}{7},\ \tan \beta =\frac{1}{3},\]then \[\cos 2\alpha =\] [CET 1986]

    A) \[\sin 2\beta \]

    B) \[\sin 4\beta \]

    C) \[\sin 3\beta \]

    D) None of these

    Correct Answer: B

    Solution :

    \[\cos 2\alpha =\frac{1-{{t}^{2}}}{1+{{t}^{2}}}=\frac{24}{25}\]{Here\[t=\tan \alpha \]} \[\sin 2\beta =\frac{2T}{1+{{T}^{2}}}=\frac{3}{5}\Rightarrow \cos 2\beta =\frac{4}{5}\]{\[T=\tan \beta \]} \[\therefore \,\,\sin 4\beta =2\sin 2\beta \cos 2\beta =2.\frac{3}{5}.\frac{4}{5}=\frac{24}{25}=\cos 2\alpha \].

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