Question

If $A+B={135}^{\circ }$ then $(1+cotA)(1+cotB)=$

• A. $0$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

The correct option is D $2$

Given $A+B={135}^{\circ }$

$⟹\cot (A+B)=\cot {135}^{\circ }$

$⟹\frac{\cot A\cot B-1}{\cot A+\cot B}=-1$

$⟹\cot A+\cot B+\cot A\cot B=+1$

$⟹\cot A+\cot B+\cot A\cot B+1=2$

$⟹\cot A(1+\cot B)+(1+\cot B)=2$

$⟹(1+\cot A)(1+\cot B)=2$