Question

if A+B=45 show that (1+Tan A) (1+tanb)=2

Answer 1

sol

A+B=45
To Prove: (1+tanA)(1+tanB)=2
Taking L.H.S
tan (A+B)=tan A+tanB/1-tanAtanB
=tan45=tanA+tanB/1-tanAtanB
=1-tanAtanB=tanA+tanB
=2=1+tanA+tanB+tanAtanB
=2=(1+tanA)(1+tanB)
Hence proved

Answer 2

Heya ,

A+B =45°(given)

now ,
tan(A+B)=Tan45°

=TanA+TanB/1-TanA●TanB=1

=TanA+TanB=1-TanA●TanB

=TanA+TanB+TabA●TanB=1
now ,adding (1) on both side

then it become

=1+TanA+TanB+TanA●TanB=1+1

=(1+TanA)+TanB(1+TanA)=2

=(1+TanA)(1+TanB)=2

hope it help you

@rajukymar☺●●●●