Question

If tan(a+b)=1 and tan(a-b)=1/root 3
Find the value of a and b

Answer 1

Answer:

Step-by-step explanation:

Tan(A+B) =1

Tan(A+B) = tan 45

(A+B) =45.......................... . 1

Tan(A-B) =1÷√3

Tan (A-B) =tan30

(A-B) = 30........................... 2

Eq1 +eq2

2A = 75

A = 37.5

B = 7.5

Answer 2

Answer: a = 37.5 and b = 7.5

Step-by-step explanation:

Here,

tan (a+b) = 1

tan(a+b) = tan(45)  ( tan 45° = 1 )

⇒ a+b = 45 -----(1)

Now, tan( a-b) = 1/√3

⇒ tan(a-b) = tan(30) ( tan 30° = 1/√3 )

⇒ a-b = 30 ------(2)

By adding equation (1) and (2)

We get,

2a = 75

⇒ a = 37.5

Substitute this value in equation (1),

We get, b = 7.5