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

  • question_answer
    If \[\sin x+\cos x=\frac{1}{5},\]then \[\tan 2x\]is [UPSEAT 2003]

    A) \[\frac{25}{17}\]

    B) \[\frac{7}{25}\]

    C) \[\frac{25}{7}\]

    D) \[\frac{24}{7}\]

    Correct Answer: D

    Solution :

    \[\sin x+\cos x=\frac{1}{5}\] Þ \[{{\sin }^{2}}x+{{\cos }^{2}}x+2\sin x\cos x=\frac{1}{25}\] \[\sin 2x=\frac{-24}{25}\] Þ \[\cos 2x=\frac{-7}{25}\] Þ \[\tan 2x=\frac{24}{7}\].

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