JEE Main & Advanced Sample Paper JEE Main - Mock Test - 42

  • question_answer
    If \[y={{\cos }^{-1}}\left( \frac{5\cos x-12\sin x}{13} \right),\] where \[x\in \left( 0,\frac{\pi }{2} \right)\], then \[\frac{dy}{dx}\] is-

    A) 1                     

    B)        -1

    C) 0                     

    D)        None of these

    Correct Answer: A

    Solution :

    [a] \[\begin{align}   & y=co{{s}^{-1}}\left[ \frac{5}{13}\cos x-\frac{12}{13}\sin x \right] \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\downarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\downarrow  \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\cos \alpha \,\,\,\,\,\,\,\,\,\,\,\,\,\,\sin \alpha  \\ \end{align}\] \[=co{{s}^{-1}}\left[ cos\left( x+\alpha  \right) \right]\] \[y=x+\alpha \text{ }y'=1\]


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