Question

Prove that :

→ ( 1 + tan A ) ( 1 + tan B ) = 2 , if A + B = 45° .

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Answer 1

Answer :

Step-by-step explanation:

For solution :

See the attachment.

Hence, it is proved.

Answer 2

$\huge\blue{ ANSWER :-}$

A+B=45°

tan(A+B)=tan45°

tan A+tan B /1-tan A tan B=1

tan A+ tan B=1-tan A+ tan B

$\boxed{\huge{\bf{ADD\:\:1\:\: BOTH \:\: SIDE}}}$

tan A + tan B + tan A + tan B +1=1+1

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

$\boxed{\huge{\bf{(1+tan B) (tan A+1}}}$

$\huge\purple{HENCE\:\:\:PROVED}$