A) \[\sqrt{2}-1\]
B) \[2\sqrt{2}\]
C) \[2\sqrt{2}-1\]
D) \[2\sqrt{2}+1\]
Correct Answer: C
Solution :
Given, an isosceles right angled triangle ABC. Then, \[\angle A=\angle C={{45}^{o}}\] and \[\angle B={{90}^{o}}\] Now, \[\tan \left( \frac{A}{2} \right)+\tan \left( \frac{B}{2} \right)+\tan \left( \frac{C}{2} \right)\] \[=\tan \left( \frac{{{45}^{o}}}{2} \right)+\tan \left( \frac{{{90}^{o}}}{2} \right)+\tan \left( \frac{{{45}^{o}}}{2} \right)\] \[=\sqrt{2}-1+1+\sqrt{2}-1\] \[\left[ \because \,\,\,\tan \left( {{22}^{o}}\frac{1}{2} \right)=\sqrt{2}-1 \right]\] \[=2\sqrt{2}-1\]You need to login to perform this action.
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