hard trig problem?

Question

tan^2(2A-pie/12) = 3 domain: 0 (greater than or equal to) A (greater than or equal to) 2pie

Answer 1

Domain:

0 ≤ A ≤ 2π

0 ≤ 2A ≤ 4π

-π/12 ≤ 2A - π/12 ≤ 4π - π/12

-15° ≤ 2A -15° ≤ 705°

Solution:

tan²(2A – π/12) = 3

tan(2A – π/12) = ±√3

There are 8 solutions in the given domain:

2A – π/12 =
2A -15° = 60°, 120°, 240°, 300°, 420°, 480°, 600° and 660°

2A = 75°, 135°, 255°, 315°, 435°, 495°, 615° and 675°

Answer:

A = 37.5°, 67.5°, 127.5°, 157.5°, 217.5°, 247.5°, 307.5° and 337.5°

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