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

  • question_answer
    \[\frac{\sin 2A}{1+\cos 2A}.\frac{\cos A}{1+\cos A}=\]

    A) \[\tan \frac{A}{2}\]

    B) \[\cot \frac{A}{2}\]

    C) \[\sec \frac{A}{2}\]

    D) \[\text{cosec}\frac{A}{2}\]

    Correct Answer: A

    Solution :

    \[\left( \frac{\sin 2A}{1+\cos 2A} \right)\,\left( \frac{\cos A}{1+\cos A} \right)\] \[=\frac{2\sin A\cos A}{2{{\cos }^{2}}A}\frac{\cos A}{1+\cos A}=\frac{\sin A}{1+\cos A}=\tan \frac{A}{2}\].

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