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JEE Main & Advanced Sample Paper JEE Main Sample Paper-15

  • question_answer
    If \[\sec (A-2B),\,\sec A,\,\sec (A+2B)\] are in A.P. then the value of \[\left( \frac{{{\cos }^{2}}A}{{{\cos }^{2}}B} \right)\]is less than

    A)  1                                            

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

    C)  2                                            

    D)  3

    Correct Answer: D

    Solution :

    \[2\sec A=\sec (A-2B),\sec A,\sec (A+2B)\] \[\frac{2}{\cos A}=\frac{\cos (A+2B)+\cos (A-2B)}{\cos (A-2B)+\cos A(A+2B)}\] \[\cos 2A+\cos 4B=\cos A(2\cos A\cos 2B)\] \[2{{\cos }^{2}}A-1+2{{\cos }^{2}}2B-1=2{{\cos }^{2}}A\cos 2B\] \[{{\cos }^{2}}A(1-\cos 2B)+(\cos 2B+1)(\cos 2B-1)=0\] \[\left( \frac{{{\cos }^{2}}A}{{{\cos }^{2}}B} \right)=2\]Ans.


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