Question

If tan (A + B) = √3 and tan (A – B) = 1, 00 < (A + B) < 900

and A < B, then find A and B.​

Answer 1

Step-by-step explanation:

$\tan( \alpha + \beta ) = \sqrt{3} \\ (\alpha + \beta ) = \frac{\pi}{3} \\ \tan( \alpha - \beta ) = 1 \\ ( \alpha - \beta ) = \frac{\pi}{4} \\ by \: adding \: we \: get, \\( \alpha + \beta) + ( \alpha - \beta ) = 2 \alpha = \frac{7\pi}{12} \\ \alpha = \frac{7\pi}{24} \\ by \: subtracting \: we \: get, \\( \alpha + \beta) - (\alpha - \beta ) = 2 \beta = \frac{\pi}{12} \\ \beta = \frac{\pi}{24}$

A =7π/24 and B =π/24 is the right answer.