Question

If A + B =45then value of (1 + tan A) (1 + tan B) equals

Answer 1

(1 + tan A )(1+ tan (45 - A)

  = (1 + tan A)  [  1 + (tan 45 - tan A)/(1+tan 45 tan A)  ]
  =  (1 + tan A)  2 / (1 + tan A ] =
 =  2


  

Answer 2

It's given, A+B=45°
→ $tan(A+B)=tan(45^{o})=1$
→ $\frac{tan(A)+tan(B)}{1-tan(A)tan(B)}=1$
→ $tan(A)+tan(B)=1-tan(A)tan(B)$
Add '1' on both the sides, then
→ $1+tan(A)+tan(B)+tan(A)tan(B)=2$
→ $[1+tan(A)][1+tan(B)]=2$