Question

if A+B= 45 degree show that (1+tan A)(1+tan B)=2​

Answer 1

Step-by-step explanation:

Given :-

A+B = 45°

To find :-

Show that (1+tan A)(1+tan B)=2

Solution:-

Given that

A+B = 45°

On taking Tangent both sides then

=> Tan (A+B) = Tan 45°

=> (Tan A+ Tan B )/(1-Tan A Tan B ) = 1

=> Tan A + Tan B = 1 - Tan A Tan B

=> Tan A + Tan B + Tan A Tan B = 1 ---------(1)

Now

On taking LHS

(1+tan A)(1+tan B)

=> 1(1+Tan B ) + Tan A ( 1+Tan B)

=> 1+Tan B + Tan A + Tan A Tan B

=> Tan A + Tan B + Tan A Tan B + 1

=> (Tan A + Tan B + Tan A Tan B )+1

=> 1+1

From (1)

=> 2

=> RHS

=> LHS = RHS

Hence, Proved.

Answer :-

If A+B = 45° then (1+tan A)(1+tan B)=2

Used formulae:-

→ Tan(A+B) = (Tan A+Tan B )/(1-Tan ATan B )

→ Tan 45° = 1