C}{\sin C}\]; \[\frac{5}{\sin \left( \frac{\pi }{2}+B \right)}=\frac{4}{\sin B}\] \[\frac{5}{\cos B}=\frac{4}{\sin B}\], \ \[\tan B=\frac{4}{5}\] \[\tan A=\tan \left( \frac{\pi }{2}+B \right)=-\cot B=\frac{-5}{4}\] \[\tan C=\tan (\pi -(A+B))\]\[=-\tan (A+B),\]\[[A+B+C=\pi ]\]        \[=-\frac{(\tan A+\tan B)}{1-\tan A.\tan B}\]\[=\frac{-\left( -\frac{5}{4}+\frac{4}{5} \right)}{1+1}=\frac{9}{40}\] \[C={{\tan }^{-1}}\left( \frac{\left( 2.\frac{1}{9} \right)}{1-{{\left( \frac{1}{9} \right)}^{2}}} \right)\];  \ \[C=2{{\tan }^{-1}}\left( \frac{1}{9} \right)\].

"> C}{\sin C}\]; \[\frac{5}{\sin \left( \frac{\pi }{2}+B \right)}=\frac{4}{\sin B}\] \[\frac{5}{\cos B}=\frac{4}{\sin B}\], \ \[\tan B=\frac{4}{5}\] \[\tan A=\tan \left( \frac{\pi }{2}+B \right)=-\cot B=\frac{-5}{4}\] \[\tan C=\tan (\pi -(A+B))\]\[=-\tan (A+B),\]\[[A+B+C=\pi ]\]        \[=-\frac{(\tan A+\tan B)}{1-\tan A.\tan B}\]\[=\frac{-\left( -\frac{5}{4}+\frac{4}{5} \right)}{1+1}=\frac{9}{40}\] \[C={{\tan }^{-1}}\left( \frac{\left( 2.\frac{1}{9} \right)}{1-{{\left( \frac{1}{9} \right)}^{2}}} \right)\];  \ \[C=2{{\tan }^{-1}}\left( \frac{1}{9} \right)\].

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If in a triangle \[ABC,a=5,b=4,A=\frac{\pi }{2}+B\], then C   [Kerala (Engg.) 2005]

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) 11 months ago

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\[\because \] \[\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{C}{\sin C}\]; \[\frac{5}{\sin \left( \frac{\pi }{2}+B \right)}=\frac{4}{\sin B}\] \[\frac{5}{\cos B}=\frac{4}{\sin B}\], \ \[\tan B=\frac{4}{5}\] \[\tan A=\tan \left( \frac{\pi }{2}+B \right)=-\cot B=\frac{-5}{4}\] \[\tan C=\tan (\pi -(A+B))\]\[=-\tan (A+B),\]\[[A+B+C=\pi ]\]        \[=-\frac{(\tan A+\tan B)}{1-\tan A.\tan B}\]\[=\frac{-\left( -\frac{5}{4}+\frac{4}{5} \right)}{1+1}=\frac{9}{40}\] \[C={{\tan }^{-1}}\left( \frac{\left( 2.\frac{1}{9} \right)}{1-{{\left( \frac{1}{9} \right)}^{2}}} \right)\];  \ \[C=2{{\tan }^{-1}}\left( \frac{1}{9} \right)\].

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Posted on 31 Aug 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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