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sin-9-sin-21-sin-39-2-golden-ratio-m-n-




Question Number 153553 by mnjuly1970 last updated on 08/Sep/21
   sin(9) + sin(21)+sin(39)=^? (ϕ/( (√2)))     ϕ:= golden ratio   m.n
sin(9)+sin(21)+sin(39)=?φ2φ:=goldenratiom.n
Answered by bramlexs22 last updated on 08/Sep/21
 sin (9°)+sin (21°)+sin (39°)=   2sin 15° cos 6°+sin (45°−6°)=   2sin (45°−30°)cos 6°+((√2)/2) cos 6°−((√2)/2) sin 6°=   2cos 6°(((√6)/4)−((√2)/4))+((√2)/2)cos 6°−((√2)/2)sin 6° =  ((√6)/2) cos 6°−((√2)/2)sin 6° = (√((6+2)/4)) cos (6°−330°)  =(√2) cos 324°=(√2) cos (270°+54°)  =(√2) sin 54° = (√2) cos 36°  =(√2) (1−2sin^2 18°)  =(√2)(1−2((((√5)−1)/4))^2 )=(√2) (1−(((6−2(√5))/8)))  =(√2) (((2+2(√5))/8))=(√2)((((√5)+1)/4))=((√2)/2)((((√5)+1)/2))  =(1/( (√2)))ϕ=(ϕ/( (√2)))
sin(9°)+sin(21°)+sin(39°)=2sin15°cos6°+sin(45°6°)=2sin(45°30°)cos6°+22cos6°22sin6°=2cos6°(6424)+22cos6°22sin6°=62cos6°22sin6°=6+24cos(6°330°)=2cos324°=2cos(270°+54°)=2sin54°=2cos36°=2(12sin218°)=2(12(514)2)=2(1(6258))=2(2+258)=2(5+14)=22(5+12)=12φ=φ2
Commented by Tawa11 last updated on 08/Sep/21
great sir
greatsir

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