Question

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

Answer 1

Answer:

• A = 45°
• B = 15°

Step-by-step explanation:

⇒tan (A + B) = √3

⇒Since √3 = tan 60°

Now substitute the degree value

⇒ tan (A + B) = tan 60°

⇒(A + B) = 60° … (i)

The above equation is assumed as equation (i)

⇒tan (A – B) = 1/√3

⇒Since 1/√3 = tan 30°

Now substitute the degree value

⇒ tan (A – B) = tan 30°

⇒(A – B) = 30° … equation (ii)

Now add the equation (i) and (ii), we get

⇒A + B + A – B = 60° + 30°

Cancel the terms B

⇒2A = 90°

⇒A= 45°

Now, substitute the value of A in equation (i) to find the value of B

⇒45° + B = 60°

⇒B = 60° – 45°

⇒B = 15°

Therefore, A = 45° and B = 15°.