11th Class Mathematics Trigonometric Identities Question Bank Critical Thinking

  • question_answer If \[{{\cos }^{6}}\alpha +{{\sin }^{6}}\alpha +K\,{{\sin }^{2}}2\alpha =1,\] then K =

    A) \[\frac{4}{3}\]

    B) \[\frac{3}{4}\]

    C) \[\frac{1}{2}\]

    D) 2

    Correct Answer: B

    Solution :

    Since \[{{\cos }^{6}}\alpha +{{\sin }^{6}}\alpha +K{{\sin }^{2}}2\alpha =1\] using formula \[{{a}^{3}}+{{b}^{3}}={{(a+b)}^{3}}-3ab(a+b)\] and on solving, we get the required result i.e. \[K=\frac{3}{4}\].


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