Question

If `tan (A + B) = sqrt(3)` and `tan (A - B) = 1/sqrt(3)`, A > B, then the value of A is ______.

Answer 1

If `tan (A + B) = sqrt(3)` and `tan (A - B) = 1/sqrt(3)`, A > B, then the value of A is 45°.

Explanation:

∵ `tan (A + B) = sqrt(3) = tan 60^circ`

Hence, A + B =  60°   ...(i)

Again, `tan (A - B) = 1/sqrt(3) = tan 30^circ`

⇒ A – B = 30°   ...(ii)

Adding equations (i) and (ii), we get

2A = 90°

⇒ A = 45°