proof left as an exercise

06082022, 01:50 AM
Post: #6




RE: proof left as an exercise
Another proof, letting t = tan(10°)
tan(30°) = 1/√3 = (3tt³) / (13t²) // tripleangle formula ⇒ t³ = √3*t² + 3t  1/√3 ⇒ t^{4} = 6t² + 8/√3*t  1 2*cos(30°) / (1 + 4*cos(20°)) ?=? tan(20°) √3 / (1 + 4*(1t²)/(1+t²)) ?=? 2t / (1t²) // tangent halfangle formula √3*(1+t²) / (53t²) ?=? 2t / (1t²) // cross multiply √3*(1t^{4}) ?=? 10t  6t³ √3*(1t^{4}) + 6t³  10t = √3  √3*(6t² + 8/√3*t  1) + 6*(√3*t² + 3t  1/√3)  10t = 0 QED 

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Messages In This Thread 
proof left as an exercise  Thomas Klemm  06062022, 11:41 PM
RE: proof left as an exercise  Ángel Martin  06072022, 05:05 AM
RE: proof left as an exercise  Thomas Klemm  06072022, 05:32 AM
RE: proof left as an exercise  Albert Chan  06072022, 05:36 PM
RE: proof left as an exercise  Albert Chan  06072022, 06:17 PM
RE: proof left as an exercise  Albert Chan  06082022 01:50 AM
RE: proof left as an exercise  Albert Chan  06082022, 11:12 AM
RE: proof left as an exercise  Thomas Klemm  06082022, 11:18 PM
RE: proof left as an exercise  Albert Chan  06092022, 12:35 AM
RE: proof left as an exercise  Albert Chan  07012022, 07:51 PM
RE: proof left as an exercise  Albert Chan  07022022, 11:44 PM

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