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

  • question_answer
    \[\frac{\sin \theta +\sin 2\theta }{1+\cos \theta +\cos 2\theta }=\] [Roorkee 1971]

    A) \[\frac{1}{2}\tan \theta \]

    B) \[\frac{1}{2}\cot \theta \]

    C) \[\tan \theta \]

    D) \[\cot \theta \]

    Correct Answer: C

    Solution :

    \[\frac{\sin \theta +\sin 2\theta }{1+\cos \theta +\cos 2\theta }\] \[=\frac{\sin \theta +2\sin \theta \cos \theta }{2{{\cos }^{2}}\theta +\cos \theta }=\frac{\sin \theta (1+2\cos \theta )}{\cos \theta (1+2\cos \theta )}=\tan \theta \]. Trick: Put\[\theta =30{}^\circ \], since for \[\theta =30{}^\circ \]no option will give the common value.

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