11th Class Mathematics Trigonometric Identities Question Bank Critical Thinking

  • question_answer Let A, B and C are the angles of a plain triangle and \[\tan \frac{A}{2}=\frac{1}{3},\,\,\tan \frac{B}{2}=\frac{2}{3}\]. Then \[\tan \frac{C}{2}\] is equal to   [Orissa JEE 2003]

    A) 7/9

    B) 2/9

    C) 1/3

    D) 2/3

    Correct Answer: A

    Solution :

    \[A+B+C=\pi \] \[\therefore \,\,\,\tan \left( \frac{A+B}{2} \right)=\tan \left( \frac{\pi }{2}-\frac{C}{2} \right)\] Þ \[\frac{\tan \frac{A}{2}+\tan \frac{B}{2}}{1-\tan \frac{A}{2}.\tan \frac{B}{2}}=\cot \frac{C}{2}\Rightarrow \frac{\frac{1}{3}+\frac{2}{3}}{1-\frac{1}{3}.\frac{2}{3}}=\frac{9}{7}=\cot \frac{C}{2}\] \ \[\tan \frac{C}{2}=\frac{7}{9}\].

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