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SSC Sample Paper Mock Test-12 SSC CGL Tear-II Paper-1

  • question_answer
    If \[\cos x+{{\cos }^{2}}x=1,\] then the value of \[{{\sin }^{8}}x+2{{\sin }^{6}}x+{{\sin }^{4}}x\] is

    A) 0

    B)  \[-1\]

    C)  2

    D)  1  

    Correct Answer: D

    Solution :

    As,        \[\cos x=1-{{\cos }^{2}}x\] \[={{\sin }^{2}}x\] \[{{\sin }^{8}}x+2{{\sin }^{6}}x+{{\sin }^{4}}x={{(\cos x)}^{4}}+2{{\cos }^{3}}x+{{\cos }^{2}}x\]            \[={{({{\cos }^{2}}x+\cos x)}^{2}}\] [from Eq.(i)] \[={{(1)}^{2}}=1\]


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