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

  • question_answer
    In any triangle ABC, the value of \[a({{b}^{2}}+{{c}^{2}})\cos A+b({{c}^{2}}+{{a}^{2}})\cos B+c({{a}^{2}}+{{b}^{2}})\cos C\]is [MP PET 1994]

    A) \[3ab{{c}^{2}}\]

    B) \[3{{a}^{2}}bc\]

    C) \[3abc\]

    D) \[3a{{b}^{2}}c\]

    Correct Answer: C

    Solution :

    \[a{{b}^{2}}\cos A+b{{a}^{2}}\cos B+a{{c}^{2}}\cos A+c{{a}^{2}}\cos C\]\[+b{{c}^{2}}\cos B+{{b}^{2}}c\cos C\] \[=ab(b\cos A+a\cos B)+ac\text{ }c\,(\cos A+a\cos C)\]\[+bc(c\cos B+b\cos C)\]= \[abc+abc+abc=3abc\].


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