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JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

  • question_answer
    If \[\sin A,\cos A\] and \[\tan A\] are in G.P., then \[{{\cos }^{3}}A+{{\cos }^{2}}A\] is equal to

    A) 1

    B) 2

    C) 4

    D) None of these

    Correct Answer: A

    Solution :

    We have \[\sin A,\,\cos A\] and \[\tan A\] are in G.P. \[{{\cos }^{2}}A=\sin A\,\tan A=\frac{{{\sin }^{2}}A}{\cos A}\,\Rightarrow \,{{\cos }^{3}}A-{{\sin }^{2}}A=0\] Hence \[{{\cos }^{3}}A+{{\cos }^{2}}A={{\sin }^{2}}A+{{\cos }^{2}}A=1\]


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