Question

A+B=45°,(1-COTA)(1-COTB)=2

Answer 1

$\cot(a + b) = \frac{ \cot(a) \cot(b) - 1 }{ \cot(a) + \cot(b) } \\ 1 = \frac{ \cot(a) \cot(b) - 1}{ \cot(a) + \cot(b) } \\ \cot(a) + \cot(b) = cot(a)cot(b) - 1$
Now
$(1 - cot(a))(1 - cot(b)) \\ 1 + cotacotb - cota - cotb$
putting value
$of \: cota + cotb \: you \: will \\ get \: 2 \: as \: a \: answer$