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proof left as an exercise
06-08-2022, 11:12 AM
Post: #7
RE: proof left as an exercise
(06-08-2022 01:50 AM)Albert Chan Wrote:  Another proof, letting t = tan(10°)

tan(30°) = 1/√3 = (3t-t³) / (1-3t²)                  // triple-angle formula
⇒ t³ = √3*t² + 3t - 1/√3

We could simplify previous proof, by getting t² in terms of t

t²*t = √3*t² + 3t - 1/√3
t² = (3t - 1/√3) / (t - √3)

2*cos(30°) / (1 + 4*cos(20°))
= √3 / (1 + 4*(1-t²)/(1+t²))
= (1/√3 - t) / (1 + (1/√3)*t)
= (tan(30°) - tan(10°)) / (1 + tan(30°)*tan(10°))
= tan(20°)
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Messages In This Thread
proof left as an exercise - Thomas Klemm - 06-06-2022, 11:41 PM
RE: proof left as an exercise - Albert Chan - 06-08-2022 11:12 AM



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