Question

If A +B = $\frac{\pi }{4},$ then value of $(1-cotA)(1-cotB)$ is equal to:

Answer 1

$A+B=\frac{\pi }{4}=\frac{180}{4}=45°A+B=45°\therefore cot(A+B)=cot45°$

$\therefore \frac{(cotB+cotA)}{cotBcotA-1}=1\Rightarrow cotB+cotA=cotBcotA=1\Rightarrow cotB+cotA-cotBcotA+1=0\Rightarrow cotBcotA-cotB-cotA-1=0\Rightarrow cotBcotA-cotB-cotA-1+2=0+2\Rightarrow cotBcotA-cotB-cotA+1=2\Rightarrow cotB(cotA-1)(cotA-1)=2\Rightarrow (cotA-1)(cotB-1)=2$

Proved