FRAC{2\cos A}{a}+\frac{\cos B}{b}+\frac{2\cos C}{c}=\frac{a}{bc}+\frac{b}{CA}\] Þ  \[\frac{2({{b}^{2}}+{{c}^{2}}-{{a}^{2}})}{2abc}+\frac{{{a}^{2}}+{{c}^{2}}-{{b}^{2}}}{2abc}+\frac{2({{a}^{2}}+{{b}^{2}}-{{c}^{2}})}{2abc}\]\[=\frac{a}{bc}+\frac{b}{ca}\] Þ\[\frac{3{{b}^{2}}+{{c}^{2}}+{{a}^{2}}}{2abc}\]\[=\frac{a}{bc}+\frac{b}{ca}\]Þ\[\frac{3b}{2ac}+\frac{c}{2AB}+\frac{a}{2bc}=\frac{a}{bc}+\frac{b}{ca}\] Þ \[{{b}^{2}}+{{c}^{2}}={{a}^{2}}\]. Hence\[\angle A={{90}^{o}}\].

"> FRAC{2\cos A}{a}+\frac{\cos B}{b}+\frac{2\cos C}{c}=\frac{a}{bc}+\frac{b}{CA}\] Þ  \[\frac{2({{b}^{2}}+{{c}^{2}}-{{a}^{2}})}{2abc}+\frac{{{a}^{2}}+{{c}^{2}}-{{b}^{2}}}{2abc}+\frac{2({{a}^{2}}+{{b}^{2}}-{{c}^{2}})}{2abc}\]\[=\frac{a}{bc}+\frac{b}{ca}\] Þ\[\frac{3{{b}^{2}}+{{c}^{2}}+{{a}^{2}}}{2abc}\]\[=\frac{a}{bc}+\frac{b}{ca}\]Þ\[\frac{3b}{2ac}+\frac{c}{2AB}+\frac{a}{2bc}=\frac{a}{bc}+\frac{b}{ca}\] Þ \[{{b}^{2}}+{{c}^{2}}={{a}^{2}}\]. Hence\[\angle A={{90}^{o}}\].

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In a triangle \[ABC\], \[\frac{2\cos A}{a}+\frac{\cos B}{b}+\frac{2\cos C}{c}=\] \[\frac{a}{bc}+\frac{b}{ca}\], then the value of angle A is [IIT 1993]

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) 10 months ago

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\[\FRAC{2\cos A}{a}+\frac{\cos B}{b}+\frac{2\cos C}{c}=\frac{a}{bc}+\frac{b}{CA}\] Þ  \[\frac{2({{b}^{2}}+{{c}^{2}}-{{a}^{2}})}{2abc}+\frac{{{a}^{2}}+{{c}^{2}}-{{b}^{2}}}{2abc}+\frac{2({{a}^{2}}+{{b}^{2}}-{{c}^{2}})}{2abc}\]\[=\frac{a}{bc}+\frac{b}{ca}\] Þ\[\frac{3{{b}^{2}}+{{c}^{2}}+{{a}^{2}}}{2abc}\]\[=\frac{a}{bc}+\frac{b}{ca}\]Þ\[\frac{3b}{2ac}+\frac{c}{2AB}+\frac{a}{2bc}=\frac{a}{bc}+\frac{b}{ca}\] Þ \[{{b}^{2}}+{{c}^{2}}={{a}^{2}}\]. Hence\[\angle A={{90}^{o}}\].

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Posted on 17 Sep 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Mathematics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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