Question

a+c=135 then find
(1+cota)(1+cotc)

Answer 1

a + c = 135°

take both sides tan

tan( a + c) = tan135° = tan( 180° -45°)

( tana + tanc )/( 1 - tana.tanc) = -1

( tana + tanc ) = -1 + tana.tanc

1/cota + 1/cotc = -1 + 1/cota.cotc

cota + cotc = -cota.cotc + 1

cota + cotc + cota.cotc +1 = 1 +1

cota + 1 + cotc ( 1 + cota) = 2

( cota + 1)(cotc +1) = 2

hence,

( 1 + cota )( 1 + cotc ) = 2