2. Solved Papers
  3. J & K CET Engineering

J & K CET Engineering J and K - CET Engineering Solved Paper-2012

  • question_answer
    If \[A+B+C=\pi \] and \[\sin C+\sin A\,\cos B=0,\] then \[\tan \,A.\,\cot \,B\] is equal to

    A)  \[0\]

    B)  \[-\frac{1}{2}\]

    C)  \[1\]

    D)  \[-1\]

    Correct Answer: B

    Solution :

    Given,   \[A+B+C=\pi \] Also,   \[\sin \,C+sin\,A\,cos\,B=0\] \[\therefore \]\[\sin \,[\pi -(A+B)]+\sin A\,\cos B=0\] \[\Rightarrow \] \[\sin (A+B)\,+\sin A\,\cos \,B=0\] \[\Rightarrow \]\[\sin A\,\cos B+\cos A\,\sin B+\sin A\,\cos B=0\] \[\Rightarrow \]\[-2\sin A\,\cos B=\cos A\,\sin B\] \[\therefore \]\[\tan A\,\cot B=\frac{\sin A}{\cos A}.\frac{\cos B}{\sin B}\] \[=\frac{\sin A\cos \,B}{-2\sin \,A\,\cos B}=-\frac{1}{2}\]


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