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

  • question_answer
    \[2\sin A{{\cos }^{3}}A-2{{\sin }^{3}}A\cos A=\] [Roorkee 1975; Kerala (Engg.) 2001]

    A) \[\sin 4A\]

    B) \[\frac{1}{2}\sin 4A\]

    C) \[\frac{1}{4}\sin 4A\]

    D) None of these

    Correct Answer: B

    Solution :

    \[2\sin A{{\cos }^{3}}A-2{{\sin }^{3}}A\cos A\]\[=2\sin A\cos A({{\cos }^{2}}A-{{\sin }^{2}}A)\] \[=2\sin A\cos A\cos 2A=\sin 2A\cos 2A=\frac{1}{2}\sin 4A\].


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