Question

IF A+B = π/4
• Prove that
(1 + tan A) (1+ tanB) = 2​

Answer 1

Step-by-step explanation:

A+B=π/4

taking tan in both side,

=>tan(A+B)=tan(π/4)

=>(tanA+tanB)/1-tanAtanB=1

=>tanA+tanB=1-tanAtanB

=>tanA+tanB+tanAtanB=1

=>tanA+tanB+tanAtanB+1=2

=>(tanA+1)+tanB(tanA+1)=2

=>(1+tanA)(1+tanB)=2 [proved)