2007-04-10 05:15:54 · 3 answers · asked by harisha_friends 1 in Science & Mathematics ➔ Mathematics
x=18
2x=36
3x=54
sin2x = sin 36 = sin(90-54) =cos 54 = cos 3x
therefore
sin2x = cos 3x
2sinx cosx = 4(cosx)^3 - 3 cosx
cancel off cosx
2sinx = 4(cosx)^2 - 3
use (cosx)^2 = 1 - (sinx)^2
2sinx = 4[1 - (sinx)^2] - 3
simplify into a quadratic in sin x and solve
4(sinx)^2 + 2 sinx -1 = 0
solving and taking the positive value
sin 18 = [sqrt(5) -1] / 4 ,
the angles in degrees
2007-04-10 05:40:38 · answer #1 · answered by qwert 5 · 1⤊ 0⤋
5*18=90
2x=36
3x=54
sin18=cos(90-18)=cos72
2sin18 cos18=4cos^3 18-3 cos 18
Try to complete the solution
2007-04-10 05:24:23 · answer #2 · answered by iyiogrenci 6 · 0⤊ 0⤋
find sin 18 frm relationship sin2xcos3x
2016-02-01 06:53:55 · answer #3 · answered by Andromache 4 · 0⤊ 0⤋
Er... sin(2x) = cos(3x), or for that matter sin^2(x) = cos^3(x) doesn't really make sense. Sorry there.
2007-04-10 05:29:51 · answer #4 · answered by jeremykong2 2 · 0⤊ 0⤋