proof left as an exercise
|
06-08-2022, 01:50 AM
Post: #6
|
|||
|
|||
RE: proof left as an exercise
Another proof, letting t = tan(10°)
tan(30°) = 1/√3 = (3t-t³) / (1-3t²) // triple-angle formula ⇒ t³ = √3*t² + 3t - 1/√3 ⇒ t4 = 6t² + 8/√3*t - 1 2*cos(30°) / (1 + 4*cos(20°)) ?=? tan(20°) √3 / (1 + 4*(1-t²)/(1+t²)) ?=? 2t / (1-t²) // tangent half-angle formula √3*(1+t²) / (5-3t²) ?=? 2t / (1-t²) // cross multiply √3*(1-t4) ?=? 10t - 6t³ √3*(1-t4) + 6t³ - 10t = √3 - √3*(6t² + 8/√3*t - 1) + 6*(√3*t² + 3t - 1/√3) - 10t = 0 QED |
|||
« Next Oldest | Next Newest »
|
Messages In This Thread |
proof left as an exercise - Thomas Klemm - 06-06-2022, 11:41 PM
RE: proof left as an exercise - Ángel Martin - 06-07-2022, 05:05 AM
RE: proof left as an exercise - Thomas Klemm - 06-07-2022, 05:32 AM
RE: proof left as an exercise - Albert Chan - 06-07-2022, 05:36 PM
RE: proof left as an exercise - Albert Chan - 06-07-2022, 06:17 PM
RE: proof left as an exercise - Albert Chan - 06-08-2022 01:50 AM
RE: proof left as an exercise - Albert Chan - 06-08-2022, 11:12 AM
RE: proof left as an exercise - Thomas Klemm - 06-08-2022, 11:18 PM
RE: proof left as an exercise - Albert Chan - 06-09-2022, 12:35 AM
RE: proof left as an exercise - Albert Chan - 07-01-2022, 07:51 PM
RE: proof left as an exercise - Albert Chan - 07-02-2022, 11:44 PM
|
User(s) browsing this thread: 1 Guest(s)