Question

If A+B=135° then prove (1+tanA)(1+tanB)=2tanA×tanB​

Answer 1

Heya

Formula

Tan ( A + B ) ={ Tan A + Tan B }/1- Tan A × Tan B

=>

Tan A + Tan B = Tan ( A + B ) × { 1 - Tan A × Tan B }

=>

Tan A + Tan B = Tan (135° ) × { 1 - Tan A × Tan ( B )

=>

Tan A + Tan B = Tan A × Tan B - 1

Becoz Tan ( 135 ) = -1

=>

Now in our question.

L.H.S

( 1 + Tan A ) × ( 1 + Tan B ) =

1 + Tan A × Tan B + Tan A + Tan B

=>

1 +Tan A × Tan B + Tan A × Tan B - 1

= 2 Tan A × Tan B

HENCE, proved.