Question

if tan (A+B) = root3 and tan (A-B) = 1/root3, find A and B

Answer 1

Given :-

• If tan (A + B) = √3 and,

• tan (A - B) = 1/√3

To find :-

• Value of A and B

Solution :-

tan (A + B) = √3

tan(A + B) = tan 60°

A + B = 60° ............................. (i)

and,

tan(A - B) = 1/√3

tan(A - B) = tan30°

A - B = 30° .............................(ii)

Adding equation (i) and (ii),

(A + B) + (A - B) = 60 + 30

⤇ A + A + B - B = 90

⤇ 2A = 90

⤇ A = 90/2

⤇ A = 45°

Putting the value of A in equation (i),

A + B = 60

⤇ 45 + B = 60

⤇ B = 60 - 45

⤇ B = 15°

Hence,the value of A and B will be 45° and 15°