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

  • question_answer
    If in a triangle, \[a{{\cos }^{2}}\frac{C}{2}+c{{\cos }^{2}}\frac{A}{2}=\frac{3b}{2},\]then its sides will be in                     [MP PET 1982; AMU 2000; AIEEE 2003]

    A) A. P.

    B) G. P.

    C) H. P.

    D) A. G.

    Correct Answer: A

    Solution :

    \[a\frac{s(s-c)}{ab}+c\frac{s(s-a)}{bc}=\frac{3b}{2}\] Þ \[2s(s-c+s-a)=3{{b}^{2}}\]  Þ \[2s(b)=3{{b}^{2}}\Rightarrow 2s=3b\] Þ \[a+b+c=3b\Rightarrow a+c=2b\Rightarrow a,b,c\]are in A.P.


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