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VIT Engineering VIT Engineering Solved Paper-2007

  • question_answer
    If \[\cos x+{{\cos }^{2}}x=1,\]then the value of \[{{\sin }^{12}}x+3{{\sin }^{10}}x+3{{\sin }^{8}}x+{{\sin }^{6}}x-1,\] is equal to :

    A)  2                

    B)  1

    C)  -1              

    D)  0

    Correct Answer: D

    Solution :

    \[\because \] \[\cos x+{{\cos }^{2}}x=1\] \[\Rightarrow \] \[\cos x=1-{{\cos }^{2}}x\]           \[={{\sin }^{2}}x\] \[{{\sin }^{12}}x+3{{\sin }^{10}}x+3{{\sin }^{8}}x+{{\sin }^{6}}x-1\] \[={{\cos }^{6}}x+3{{\cos }^{5}}x+3{{\cos }^{4}}x+{{\cos }^{3}}x-1\] \[={{({{\cos }^{2}}x+\cos x)}^{3}}-1=1-1=0\]


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