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JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Critical Thinking

  • question_answer
    In triangle \[ABC\]if \[\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\], then the triangle is                                   [Karnataka 1991; Pb. CET 1989]

    A) Right angled

    B) Obtuse angled

    C) Equilateral

    D) Isosceles

    Correct Answer: C

    Solution :

    \[\frac{\cos A}{\cos B}=\frac{a}{b}=\frac{\sin A}{\sin B}\] Þ \[\sin A\cos B=\sin B\cos A\] Þ \[\sin (A-B)=0\] Þ \[\sin (A-B)=\sin 0\] Þ \[A-B=0\]      Þ \[A=B\] Similarly, \[A=B=C\]. Hence it is an equilateral triangle.


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