Question

if A+B =45° , (Show that)(cotA-1) (cotB-1) =2

Answer 1

Hello!

cot (A + B) = ( cotA.cotB - 1 ) / ( cotA + cotB )

∵ cot 45° = 1

Then,

1 = ( cotA.cotB - 1 ) / ( cotA + cotB )

⇒ ( cotA.cotB - 1 ) =  ( cotA + CotB )

⇒ cotA.cotB - cotA - cotB = 1

Adding 1 both sides :
  
( cotA - 1 ).( cotB - 1 ) = 2. ---[ HENCE PROVED. ]

Cheers!