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JEE Main & Advanced Sample Paper JEE Main Sample Paper-17

  • question_answer
    If\[A+B+C=\pi \]and \[\sin \left( A+\frac{C}{2} \right)=k\sin \frac{C}{2},\]then \[\tan \frac{A}{2}\tan \frac{B}{2}\] is equal to

    A)  \[\frac{k-1}{k+1}\]                         

    B) \[\frac{k+1}{k-1}\]

    C)  \[\frac{k}{k+1}\]                             

    D)  1

    Correct Answer: D

    Solution :

     \[\frac{k}{1}=\frac{\sin \left( A+\frac{C}{2} \right)}{\sin \frac{C}{2}}\] \[\Rightarrow \]\[\frac{k+1}{k-1}=\frac{\sin \left( A+\frac{C}{2} \right)+\sin \frac{C}{2}}{\sin \left( A+\frac{C}{2} \right)-\sin \frac{C}{2}}=\cot \frac{B}{2}\cot \frac{A}{2}\]


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