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JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Self Evaluation Test - Trigonometric Function

  • question_answer
    Value of \[2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )\] \[-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1\] is

    A) 2                     

    B) 0    

    C) 4                     

    D) 6

    Correct Answer: B

    Solution :

    We have \[2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1\] \[=2[{{({{\sin }^{2}}\theta )}^{3}}+{{({{\cos }^{2}}\theta )}^{3}}]-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1\] \[=2[({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )({{\sin }^{4}}\theta +{{\cos }^{4}}\theta -{{\sin }^{2}}\theta \]\[{{\cos }^{2}}\theta )]-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1\] \[=[2{{\sin }^{4}}\theta +2{{\cos }^{4}}\theta -2{{\sin }^{2}}\theta {{\cos }^{2}}\theta ]-3{{\sin }^{4}}\theta -3{{\cos }^{4}}\theta +1\] \[=-{{({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}^{2}}+1=-{{1}^{2}}+1=-1+1=0\]


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