JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Relation between sides and angles, Solutions of triangles

  • question_answer
    If in triangle \[ABC,\cos A=\frac{\sin B}{2\sin C}\], then the triangle is                     [Orissa JEE 2002, 04; MP PET 2004]

    A) Equilateral

    B) Isosceles

    C) Right angled

    D) None of these

    Correct Answer: B

    Solution :

    \[\cos A=\frac{\sin B}{2\sin C}\Rightarrow \frac{{{b}^{2}}+{{c}^{2}}-{{a}^{2}}}{2bc}=\frac{b}{2c}\] Þ \[{{b}^{2}}+{{c}^{2}}-{{a}^{2}}-{{b}^{2}}=0\]Þ\[{{c}^{2}}={{a}^{2}}\].


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