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SSC Quantitative Aptitude Trigonometry Question Bank Trigonometry (I)

  • question_answer
    The maximum value of \[{{\sin }^{8}}\theta +{{\cos }^{14}}\theta ,\] for all real values of \[\theta \] is

    A) \[1\]

    B) \[\sqrt{2}\]

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

    D) \[0\]

    Correct Answer: A

    Solution :

    [a] f \[(\theta )=si{{n}^{8}}\theta +{{\cos }^{14}}\theta \] \[={{\sin }^{8}}\theta +{{(1-si{{n}^{2}}\theta )}^{7}}\] \[\therefore \]      \[f\,(90{}^\circ )=1+{{(1+1)}^{7}}\] [\[\because \]Maximum value of\[si{{n}^{2}}\theta =1\]] \[=1+0=1\]


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