A) -1
B) 2
C) 3
D) \[1/\sqrt{2}\]
Correct Answer: B
Solution :
Given, \[\angle C={{45}^{o}}\] \ \[A+B={{180}^{o}}-{{45}^{o}}={{135}^{o}}\] \ \[\cot (A+B)=\frac{\cot A\cot B-1}{\cot A+\cot B}\] Þ \[\cot ({{135}^{o}})=-1=\frac{\cot A\cot B-1}{\cot A+\cot B}\] Þ \[\cot A+\cot B=1-\cot A\cot B\] \[1+\cot A+\cot B+\cot A\cot B=2\] Þ \[(1+\cot A)(1+\cot B)=2\].
You need to login to perform this action.
You will be redirected in
3 sec
