Question

If a + b is equal to pi by 4 prove that 1 + 10 into 1 + tan b equal to 2

Answer 1

Answer:

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

Step-by-step explanation:

If $A+B=\frac{\pi}{4}$, prove that

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

Formula used:

$tan(A+B)=\frac{tanA+tanB}{1-tanA\:tanB}$

Given:

$A+B=\frac{\pi}{4}$

$\implies\:tan(A+B)=tan\frac{\pi}{4}$

$\implies\:\frac{tanA+tanB}{1-tanA\:tanB}=1$

$\implies\:tanA+tanB=1-tanA\:tanB$

$\implies\:tanA+tanB+tanA\:tanB=1$

Add 1 on both sides, we get

$1+tanA+tanB+tanA\:tanB=1+1$

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

$\implies\:(1+tanA)(1+tanB)=2$