If tan (A + B) = 3 and tan (A – B) = 1/3 ,0° find A B.
Yash Ghoderao
Solution:tan (A + B) = 3Since 3 = tan 60°Now substitute the degree valuetan (A + B) = tan 60°(A + B) = 60° … (i)The above equation is assumed as equation (i)tan (A – B) = 1/3Since 1/3 = tan 30°Now substitute the degree valuetan (A – B) = tan 30°(A – B) = 30° … equation (ii)Now add the equation (i) and (ii), we getA + B + A – B = 60° + 30°Cancel the terms B2A = 90°A= 45°Now, substitute the value of A in equation (i) to find the value of B45° + B = 60°B = 60° – 45°B = 15°Therefore A = 45° and B = 15°
