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Grade: 11
        
  • IN A TRIANGLE ABC given that
 
a=5   b=4   c=??????
 
If COS(A-B)=31/32
3 months ago

Answers : (1)

Arun
18618 Points
							
Dear student
 
I have attahed image in which solution is given.
 
In case of any difficulty please feel free to ask
 
\hspace{-0.45 cm}$Using $\cos\left(\frac{A-B}{2}\right) = \frac{1-\tan^2\frac{A-B}{2}}{1+\tan^2\frac{A-B}{2}} = \frac{31}{32}.\Rightarrow \tan\frac{A-B}{2} = \frac{1}{\sqrt{63}}$\\\\\\Now Using $\tan \frac{A-B}{2} = \frac{a-b}{a+b}\cot\frac{C}{2}\Rightarrow \tan \frac{C}{2}=\frac{\sqrt{63}}{9}$\\\\\\Now Using $\cos C = \frac{1-\tan^2 \frac{C}{2}}{1+\tan^2 \frac{C}{2}}\Rightarrow \cos C = \frac{1}{8}$\\\\ Now Using $c^2=a^2+b^2-2ab\cos C=36\Rightarrow c=6$
3 months ago
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