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

  • question_answer
    \[\sin 4\theta \]can be written as

    A) \[4\sin \theta (1-2{{\sin }^{2}}\theta )\sqrt{1-{{\sin }^{2}}\theta }\]

    B) \[2\sin \theta \cos \theta {{\sin }^{2}}\theta \]

    C) \[4\sin \theta -6{{\sin }^{3}}\theta \]

    D) None of these

    Correct Answer: A

    Solution :

    \[\sin 4\theta =2\sin 2\theta \cos 2\theta \] \[=2.2\sin \theta \cos \theta (1-2{{\sin }^{2}}\theta )\] \[=4\sin \theta (1-2{{\sin }^{2}}\theta )\sqrt{1-{{\sin }^{2}}\theta }\]

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