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

  • question_answer
    \[{{\cos }^{2}}A{{(3-4{{\cos }^{2}}A)}^{2}}+{{\sin }^{2}}A{{(3-4{{\sin }^{2}}A)}^{2}}=\]

    A) \[\cos 4A\]

    B) \[\sin 4A\]

    C) 1

    D) None of these

    Correct Answer: C

    Solution :

    \[{{\cos }^{2}}A{{(3-4{{\cos }^{2}}A)}^{2}}+{{\sin }^{2}}A{{(3-4{{\sin }^{2}}A)}^{2}}\] \[={{(3\cos A-4{{\cos }^{3}}A)}^{2}}+{{(3\sin A-4{{\sin }^{3}}A)}^{2}}\] \[={{(\cos 3A)}^{2}}+{{(\sin 3A)}^{2}}=1\]. Trick: Put\[A=\frac{\pi }{2},{{0}^{o}}\], the value of expression remains 1, therefore it is independent of A and is equal to 1.

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