Question

If $A+B={45}^0$ then the value of $(\cot A-1)(\cot B-1)$ is

• A. $-2$
• B. $2$
• C. $0$
• D. $-1$

Answer 1

Answer: (B)

$2$

Given $A+B={45}^0$

$\Rightarrow (\cot A-1)(\cot B-1)=(\cot A-1)\left(\cot \right(45-A)-1)=(\cot A-1)(\frac{\cot A+1}{\cot A-1}-1)=2$

therefore correct option is $B$.