JEE Main & Advanced Mathematics Sequence & Series Question Bank Self Evaluation Test - Sequences and Series

  • question_answer
    If the angles A< B<C of a triangle are in A.P., then

    A) \[{{c}^{2}}={{a}^{2}}+{{b}^{2}}-ab\]

    B) \[{{b}^{2}}={{a}^{2}}+{{c}^{2}}-ac\]

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

    D) None of these

    Correct Answer: B

    Solution :

    [b] \[A+C=2B\] and \[A+B+C=180{}^\circ \] so, \[B=60{}^\circ \] \[\therefore \,\,\,\cos \,60{}^\circ =\frac{{{a}^{2}}+{{c}^{2}}-{{b}^{2}}}{2ac}\Rightarrow \,\,{{b}^{2}}={{a}^{2}}+{{c}^{2}}-ac\]


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