If tan (A + B) = √3 and tan (A – B) = 1/√3 ,0° B, find A and B.

Dear Student

tan (A + B) = √3
Since √3 = tan60°
Now substitute the degree value
⇒tan (A + B) = tan 60°
(A + B) = 60° ... (i)


tan (A– B) = 1/√3
Since1/√3 = tan30°
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°

Thanks