Question

if A+ B =225, then the value of ( 1 + tanA)(1 + tanB) is

Answer 1

Hi ,

A + B = 225

A = 225 - B

Tan A = tan( 225 - B )

= Tan [ 180 + ( 45 - B ) ]

= Tan ( 45 - B )

= ( Tan45-tan B )/[1 + tan45tanB]

= ( 1 - tanB ) / ( 1 + tanB ) ---( 1 )

Now ,

According to the problem given ,

( 1 + tanA ) ( 1 + tanB )

= [1+ (1 - tanB)/(1+tanB )]( 1 + tan B )

[ From ( 1 ) ]

= [(1+tanB + 1-tanB )/( 1+tanB ) ](1+tanB)

= 2

I hope this helps you.

:)