A) \[1\]
B) \[\frac{1}{2}\]
C) \[-1\]
D) \[-2\]
E) \[2\]
Correct Answer: E
Solution :
Given, \[A+B=45{}^\circ \] \[\Rightarrow \] \[\cot (A+B)=1\] \[\Rightarrow \] \[\frac{\cot A\cot B-1}{\cot A+\cot B}=1\] \[\Rightarrow \] \[\cot A\cot B-(\cot A+\cot B)=1\] ?..(i) Now, \[(\cot A-1)(\cot B-1)=\cot A\cot B\] \[-(\cot A+\cot B)+1\] \[=1+1=2\] [from Eq. (i)]You need to login to perform this action.
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