JEE Main & Advanced JEE Main Paper (Held On 9 April 2016)

  • question_answer
    The number of distinct real roots of the equation,\[\left| \begin{matrix}    \cos x & \sin x & \sin x  \\    \sin x & \cos x & \sin x  \\    \sin x & \sin x & \cos x  \\ \end{matrix} \right|=0\]in the interval \[\left[ -\frac{\pi }{4},\frac{\pi }{4} \right]\]is:   JEE Main Online Paper (Held On 09 April 2016)

    A) 4

    B) 1

    C) 2                                             

    D) 3

    Correct Answer: C

    Solution :

                    \[\left| \begin{matrix}    \cos x & \sin x & \sin x  \\    \sin x & \cos x & \sin x  \\    \sin x & \sin x & \cos x  \\ \end{matrix} \right|=0\]                 \[\Rightarrow \]\[{{\cos }^{3}}x+{{\sin }^{3}}x+{{\sin }^{3}}x-3{{\sin }^{2}}x\cos x=0\] \[\Rightarrow \]\[(\cos x+\sin x+\sin x)({{\cos }^{2}}x+{{\sin }^{2}}x+{{\sin }^{2}}\]\[x-\cos x\sin x-\cos x\sin x-{{\sin }^{2}}x)=0\] \[\Rightarrow \]\[\cos x=-2\sin x\]or\[\cos x=\sin x\] \[\tan x=-\frac{1}{2}\]\[\tan =1\Rightarrow x=\pi /4\] \[x=-{{\tan }^{-1}}\frac{1}{2}\] two solutions

You need to login to perform this action.
You will be redirected in 3 sec spinner