Question

If Tan (A+B) =√3 and Tan A=1 then B=

Answer 1

Step-by-step explanation:

tan(a+b) = root3 tan(a-b)= 1/root3

We know tan 60 = root 3 and tan 30 = 1/root3

So, a+b = 60, a-b = 30

Adding the two gives

ata+b-b=60+30

2a=90

a = 45

a+b=60

45+b=60

b=15

Answer 2

Answer:

B=15

Step-by-step explanation:

Tan (A+B) =√3

Tan (A+B)=$\frac{tan A + tan B}{1-tan A tan B}$

√3=$\frac{1+tan B}{1-tan B}$

√3(1-tan B)=1+tan B

√3 - √3 tan B= 1 + tan B

√3-1= tan B+√3 tan B

√3-1= tan B (1+√3)

tan B=$\frac{\sqrt{3} -1}{\sqrt{3}+1}$

B=15