If A+B=(5π/4), then value of (1 + tan A)(1 + tan B) equals

Question

If A+B=(5π/4), then value of (1 + tan A)(1 + tan B) equals (A) 1 (B) 2 (C) -2 (D) -1

Tardigrade Admin · Accepted Answer

tan(A+B)=tan (5π/4) =tan(π+(π/4))=tan (π/4) ∴ tan A + tan B = 1 - tan A tan B ⇒ tan A + tan B + tan A tan B = 1 ⇒ (1 + tan A) + tan B (1 + tan A) = 1 + 1 (by adding 1 on both sides) ⇒ (1 + tan A) (1 +tan B) = 2

Q. If $A + B = \frac{5 π}{4}$ , then value of $(1 + t an A) (1 + t an B)$ equals

$1$

$2$

$- 2$

$- 1$

Q. If A+B=45π​, then value of (1+tanA)(1+tanB) equals

1

2

−2

−1

tan(A+B)=tan45π​ =tan(π+4π​)=tan4π​ ∴tanA+tanB=1−tanAtanB ⇒tanA+tanB+tanAtanB=1 ⇒(1+tanA)+tanB(1+tanA)=1+1 (by adding 1 on both sides) ⇒(1+tanA)(1+tanB)=2

Q. If $A + B = \frac{5 π}{4}$ , then value of $(1 + t an A) (1 + t an B)$ equals

$1$

$2$

$- 2$

$- 1$