Question

If tan(A + B) = √3 and tan(A - B)=1/√3,
0° <A+B ≤ 90° find the A and B.
​

Answer 1

Answer:

A-45

B-15

Step-by-step explanation:

A+B=60

A-B=30

Answer 2

Given;

• tan (A + B) = √3

As we know, tan 60° = √3

Thus,

we can write;

⇒ tan (A + B) = tan 60°

⇒(A + B) = 60° …… (i)

Now again given;

tan (A – B) = 1/√3

Since, tan 30° = 1/√3

Thus, we can write;

⇒ tan (A – B) = tan 30°

⇒(A – B) = 30° ….. (ii)

Adding the equation (i) and (ii), we get;

A + B + A – B = 60° + 30°

2A = 90°

A= 45°

Now, put the value of A in eq. (i) to find the value of B;

45° + B = 60°

B = 60° – 45°

B = 15°

Therefore,

A = 45° and B = 15°

_______________________________

Hope it will be helpful :)