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

  • question_answer
    \[\frac{\sin 3A-\cos \left( \frac{\pi }{2}-A \right)}{\cos A+\cos (\pi +3A)}=\]

    A) \[\tan A\]

    B) \[\cot A\]

    C) \[\tan 2A\]

    D) \[\cot 2A\]

    Correct Answer: D

    Solution :

    \[\frac{\sin 3A-\cos \left( \frac{\pi }{2}-A \right)}{\cos A+\cos (\pi +3A)}=\frac{\sin 3A-\sin A}{\cos A-\cos 3A}\] =\[\frac{2\cos 2A\sin A}{2\sin 2A\sin A}=\frac{\cos 2A}{\sin 2A}=\cot 2A\].

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