Question

if A+B=45° then (cotA-1)(cotB-1)=2 provide it

Answer 1

$a + b = 45 \\ \cot(a + b) = 1 \\ \frac{ \cot(a) \cot(b) - 1}{ \cot(a) + \cot(b) } = 1 \\ \cot(a) \cot(b) - 1 = \cot(a) + \cot(b) \\ \cot(a) \cot(b) - ( \cot(a) + \cot(b)) - 1 = 0 \\ \cot(a) \cot(b) - ( \cot(a) + \cot(b)) + 1 =2 \\ ( \cot(a) - 1)( \cot(b) - 1) = 2$