If A + B =45^ , then ( A -1)( B -1)= - Vidyadip

MCQ

If $A + B =45^{\circ}$, then $(\cot A -1)(\cot B -1)=$

A
$0$
✓
2
C
1
D
4

✓

Answer

Correct option: B.

2

(B)
$A + B =45^{\circ}$
$\Rightarrow \tan (A+B)=1$
$\Rightarrow \tan A+\tan B=1-\tan A \tan B$
$\Rightarrow \frac{1}{\cot A}+\frac{1}{\cot B}=1-\frac{1}{\cot A \cot B }$
$\Rightarrow \cot A +\cot B =\cot A \cot B -1$
$\Rightarrow \cot A \cot B -\cot A -\cot B =1$
$\Rightarrow \cot A \cot B -\cot A -\cot B +1=2$
$\Rightarrow(\cot A -1)(\cot B -1)=2$

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