Question

Hey guys genius question.If tan(A-B) = 7/24 and tan A = 4/3, where A and B are acute show that A+B = π/2​

Answer 1

Answer:

tan(A - B) = 7/2=

=> (tan A - tan B) ÷ (1 + tan A - tan B)

= 7/24

=> (4/3 - tan B) ÷ (1 - 4/3 tan B) = 7/24

=> (4 - 3 tan B) ÷ (3 + 4 tan B) = 7/24

=> 96 - 72 tan B = 21 + 78 tan B

=> tan B = 3/4

=> tan(A + B) = (tan A + tan B) ÷ (1 - tan A + tan B)

$= \frac{ \frac{4}{3} + \frac{3}{4} }{1 - \frac{4}{3} - \frac{3}{4} } \\ \\ = \frac{ \frac{4}{3} + \frac{3}{4} }{0} = \infty$

Therefore A + B = π/2 = 90°