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

  • question_answer
    In \[\Delta ABC\], \[{{a}^{2}}({{\cos }^{2}}B-{{\cos }^{2}}C)+\] \[{{b}^{2}}({{\cos }^{2}}C-{{\cos }^{2}}A)+\] \[{{c}^{2}}({{\cos }^{2}}A-{{\cos }^{2}}B)=\]

    A) 0

    B) 1

    C) \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\]

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

    Correct Answer: A

    Solution :

    \[\Sigma {{a}^{2}}({{\cos }^{2}}B-{{\cos }^{2}}C)=\Sigma {{a}^{2}}({{\sin }^{2}}C-{{\sin }^{2}}B)\]                                  \[={{k}^{2}}\Sigma {{a}^{2}}({{c}^{2}}-{{b}^{2}})=0\].


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