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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        The number of solutions of the equation\[\sqrt{1-\cos x}=\sin x,\pi <x<3\pi \] is

    A)  0                                            

    B)  1

    C)  2                                            

    D)  3

    Correct Answer: C

    Solution :

                    Since, \[1-cos\text{ }x\ge 0,\text{ }sin\text{ }x\ge 0\] Squaring, given equation, we get \[1-\cos x={{\sin }^{2}}x\] \[\Rightarrow \]               \[{{\cos }^{2}}x-\cos x=0\]           \[\Rightarrow \]               \[\cos x=0\]or\[\cos x=1\] If\[cos\text{ }x=0,\]then \[x=2n\pi +\frac{\pi }{2},n\in Z\] If \[cos\text{ }x=1,\]then \[x=2\pi k,k\in Z\] But\[sin\text{ }x\ge 0\]and\[x\in (\pi ,3\pi ),\]we get                 \[x=2\pi \]or\[x=\frac{5\pi }{2}\]


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