Answer:
A = π/6 + kπ, or A = 2π/3 + kπ
Step-by-step explanation:
tan A / (1 − tan² A) = √3 / 2
Cross multiply and simplify:
√3 (1 − tan² A) = 2 tan A
√3 − √3 tan² A = 2 tan A
3 − 3 tan² A = 2√3 tan A
0 = 3 tan² A + 2√3 tan A − 3
Solve with quadratic formula:
tan A = [ -2√3 ± √((2√3)² − 4(3)(-3)) ] / 2(3)
tan A = [ -2√3 ± √(12 + 36) ] / 6
tan A = (-2√3 ± √48) / 6
tan A = (-2√3 ± 4√3) / 6
tan A = -√3 or √3/3
Solve for A:
A = 2π/3 + kπ, or A = π/6 + kπ
