Question

If A+B=45 then (1+tanA)(1+tanB)=?

Answer 1

 Given A+B=45
  {Take tan on both the sides }

tan(A+B) = tan45

tanA+tanB/1- tanA tanB = 1

tanA+tanB=1-tanA.tanB

tanA+tanB+tanA.tanB=1

adding "1" on both sides

1+ tanA+tanB+tanA.tanB=1+1

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

(1+tanA)(1+tanB)=2   Hence proved .

hope it's help u

Answer 2

Given: A+B= 45

To find: $(1+\tan A) (1+\tan B)$

Step-by-step explanation:

As given

$A+B= 45$

Taking tan both side

$\tan (A+B) = \tan 45$

As we know  $\tan (A+B) = \dfrac{\tan A + \tan B}{1- \tan A \tan B}$

Therefore

$\Rightarrow \dfrac{\tan A + \tan B}{1- \tan A \tan B}=1\\\\\Rightarrow \tan A + \tan B=1- \tan A \tan B\\\\\Rightarrow \tan A + \tan B+\tan A \tan B=1$

Adding 1 both side we get

$\\\\\Rightarrrow 1+ \tan A +\tan B +\tan A \tan B=1+1\\\\\Rightarrow (1+ \tan A )+\tan B (1 +\tan A )=2\\\\\Rightarrow (1+\tan A)(1+\tan B) = 2$

Hence, the value of $(1+\tan A) (1+\tan B)$ is 2