JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Critical Thinking

  • question_answer
    In a \[\Delta ABC,\] if \[(\sin A+\sin B+\sin C)\] \[(\sin A+\sin B-\sin C)\] = \[3\sin A\sin B,\]  then the angle C is equal to [AMU 1999]

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

    B) \[\frac{\pi }{3}\]

    C) \[\frac{\pi }{4}\]

    D) \[\frac{\pi }{6}\]

    Correct Answer: B

    Solution :

    \[(a+b+c)(a+b-c)=3ab\]      Þ \[\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2ab}=\frac{1}{2}\,\,\Rightarrow \cos C=\cos \frac{\pi }{3}\Rightarrow \angle C=\pi /3\]


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