JEE Main & Advanced Sample Paper JEE Main - Mock Test - 23

  • question_answer
    The solution of the differential equation \[\tan y\frac{dy}{dx}=\sin (x+y)+sin(x-y)\] is

    A) \[\sec y-2\cos x=c\]

    B) \[\sec y+2\cos x=c\]

    C) \[\cos y-2\sin x=c\]

    D) \[\sec y+2\sin x=c\]

    Correct Answer: B

    Solution :

    [b]: Given, \[\tan y\frac{dy}{dx}=\sin (x+y)+sin(x-y)\] \[\tan y\frac{dy}{dx}=\sin (x+y)+\sin (x-y)\]\[=2\sin x\cos y\] \[\Rightarrow \]\[\tan y\sec ydy=2\sin xdx\] \[\Rightarrow \]\[\int_{{}}^{{}}{\tan y\sec ydy=2}\int_{{}}^{{}}{\sin xdx}\] \[\Rightarrow \]\[\sec y=-2\cos x+c\Rightarrow \sec y+2\cos x=c\]

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