B\]and \[\cot C\]are in A. P. Þ  \[\cot A+\cot C=2\cot B\] Þ \[\frac{\cos A}{\SIN A}+\frac{\cos C}{\sin C}=\frac{2\cos B}{\sin B}\] Þ  \[\frac{{{b}^{2}}+{{c}^{2}}-{{a}^{2}}}{2bc(ka)}+\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2ab(kc)}=2\frac{{{a}^{2}}+{{c}^{2}}-{{b}^{2}}}{2ac(kb)}\] Þ \[{{a}^{2}}+{{c}^{2}}=2{{b}^{2}}\]. HENCE\[{{a}^{2}},{{b}^{2}},{{c}^{2}}\]are in A. P. NOTE : Students should remember this question as a FACT.

"> B\]and \[\cot C\]are in A. P. Þ  \[\cot A+\cot C=2\cot B\] Þ \[\frac{\cos A}{\SIN A}+\frac{\cos C}{\sin C}=\frac{2\cos B}{\sin B}\] Þ  \[\frac{{{b}^{2}}+{{c}^{2}}-{{a}^{2}}}{2bc(ka)}+\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2ab(kc)}=2\frac{{{a}^{2}}+{{c}^{2}}-{{b}^{2}}}{2ac(kb)}\] Þ \[{{a}^{2}}+{{c}^{2}}=2{{b}^{2}}\]. HENCE\[{{a}^{2}},{{b}^{2}},{{c}^{2}}\]are in A. P. NOTE : Students should remember this question as a FACT.

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In\[\Delta ABC,\]if \[\cot A,\cot B,\cot C\]be in A. P., then \[{{a}^{2}},\text{ }{{b}^{2}},\text{ }{{c}^{2}}\] are in [MP PET 1997]

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

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\[\cot A,\cot B\]and \[\cot C\]are in A. P. Þ  \[\cot A+\cot C=2\cot B\] Þ \[\frac{\cos A}{\SIN A}+\frac{\cos C}{\sin C}=\frac{2\cos B}{\sin B}\] Þ  \[\frac{{{b}^{2}}+{{c}^{2}}-{{a}^{2}}}{2bc(ka)}+\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2ab(kc)}=2\frac{{{a}^{2}}+{{c}^{2}}-{{b}^{2}}}{2ac(kb)}\] Þ \[{{a}^{2}}+{{c}^{2}}=2{{b}^{2}}\]. HENCE\[{{a}^{2}},{{b}^{2}},{{c}^{2}}\]are in A. P. NOTE : Students should remember this question as a FACT.

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Posted on 15 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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