2. Solved Papers
  3. BCECE Engineering

BCECE Engineering BCECE Engineering Solved Paper-2013

  • question_answer
    If \[x\in \left( \frac{3\pi }{2},2\pi  \right),\]then the value of the expression \[{{\sin }^{-1}}[\cos \{{{\cos }^{-1}}(\cos x)\}+{{\sin }^{-1}}(\sin x)],\]is

    A)  \[-\frac{\pi }{2}\]                            

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

    C)  0                            

    D)         \[\pi \]

    Correct Answer: B

    Solution :

    \[\because \]     \[x\in \left( \frac{3\pi }{2},2\pi  \right)\] Now,     \[{{\cos }^{-1}}(\cos x)=2\pi -x\] and        \[{{\sin }^{-1}}(\sin x)=x-2\pi \] \[\therefore \]  \[{{\cos }^{-1}}(\cos x)+{{\sin }^{-1}}(\sin x)=0\] Therefore, \[{{\sin }^{-1}}[\cos \{{{\cos }^{-1}}(\cos x)+{{\sin }^{-1}}(\sin x)\}]\] \[={{\sin }^{-1}}\{cos(0)\}=si{{n}^{-1}}(1)=\frac{\pi }{2}\]


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