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

  • question_answer
    The value of \[2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1\] is  [MP PET 1997; UPSEAT 2002]

    A) 2

    B) 0

    C) 4

    D) 6

    Correct Answer: B

    Solution :

    \[{{({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}^{3}}={{(1)}^{3}}\] \[\Rightarrow \,\,{{\sin }^{6}}\theta +{{\cos }^{6}}\theta +3\,{{\sin }^{2}}\theta \,{{\cos }^{2}}\theta =1\] and \[{{\sin }^{4}}\theta +{{\cos }^{4}}\theta +2\,{{\sin }^{2}}\theta \,{{\cos }^{2}}\theta =1\] Both gives, \[2\,\,({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-3\,({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1=0\].


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