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[SPAM] Re: [obm-l] Dúvidas
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- Subject: [SPAM] Re: [obm-l] Dúvidas
- From: "Alex pereira Bezerra" <alexmatematica1234@xxxxxxxxx>
- Date: Sun, 15 Jun 2008 20:15:42 -0300
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a quest=E3o =E9 tg(3pi/11) + 4sen(2pi/11)=3D raiz quadrada de 11,
Vamos l=E1: Tome p =3D pi/11, e tome c=3Dcosp, s =3D senp, ent=E3o c + is=
=3D e^pi e
tamb=E9m ( c+ is)^11 =3D -1, isto =E9 c^11 +11c^10si - 55c^9s^2 - 165c^8s^3=
i +
370c^7s^4 + 462c^6s^5i - 462c^5s^6 -
330c^4s^7i+165c^3s^8+55c^2s^9i-11cs^10-s^11i=3D-1. Agora , 11c^10s- 165c^8=
s^3
+ 462c^6s^5 - 330c^4s^7+55c^2s^9-s^11=3D-1 e como s diferente de zero, tem=
os:
11c^10- 165c^8s^2 + 462c^6s^4 - 330c^4s^6+55c^2s^8-s^10=3D-1 e c^2 =3D 1 =
-
s^2, dai fica:
11- 220s^2+1232s^4-2816s^6+ 2816s^8-1024s^10=3D0 e ent=E3o
(11s-44s^3+32s^2)^2 -11c^2(1-4s^2)^2 =3D 121s^2 -968s^4
+2640s^6-2816s^8+1024s^10=3D0,isto prova que:
11s-44s^3+32s^5/c(1-4s^2) =3D +- raiz(11).
tg3p+4sin2p=3D 3tgp-tg^3p/1-3tg^2p + 8senpcosp =3D 3cs^2 -s^3/c^3-3s^2c + 8=
sc
que implica em:
tg3p + 4sin2p =3D 11s-44s^3+32s^5/c(1-4s^2) logo tg3p + 4sen2p =3D +-raiz d=
e 11,
dai como tg3p > 0 e sen2p > 0, n=F3s temos que : tg3pi/11 + 4sen2pi/11 =3D =
raiz
de 11
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<div><br><br>a quest=E3o =E9 tg(3pi/11) + 4sen(2pi/11)=3D raiz quadrada de =
11,</div>
<div>Vamos l=E1: Tome p =3D pi/11, e tome c=3Dcosp, s =3D senp, ent=E3o c +=
is=3D e^pi e tamb=E9m ( c+ is)^11 =3D -1, isto =E9 c^11 +11c^10si - 55c^9s=
^2 - 165c^8s^3i + 370c^7s^4 + 462c^6s^5i - 462c^5s^6 - 330c^4s^7i+165c^3s^8=
+55c^2s^9i-11cs^10-s^11i=3D-1. Agora , 11c^10s- 165c^8s^3 + 462=
c^6s^5 - 330c^4s^7+55c^2s^9-s^11=3D-1 e como s diferente de zero, temo=
s: 11c^10- 165c^8s^2 + 462c^6s^4 - 330c^4s^6+55c^2s^8-s^10=
=3D-1 e c^2 =3D 1 - s^2, dai fica:</div>
<div>11- 220s^2+1232s^4-2816s^6+ 2816s^8-1024s^10=3D0 e ent=E3o</div>
<div>(11s-44s^3+32s^2)^2 -11c^2(1-4s^2)^2 =3D 121s^2 -968s^4 +2640s^6-2816s=
^8+1024s^10=3D0,isto prova que:</div>
<div>11s-44s^3+32s^5/c(1-4s^2) =3D +- raiz(11).</div>
<div>tg3p+4sin2p=3D 3tgp-tg^3p/1-3tg^2p + 8senpcosp =3D 3cs^2 -s^3/c^3-3s^2=
c + 8sc que implica em:</div>
<div>tg3p + 4sin2p =3D 11s-44s^3+32s^5/c(1-4s^2) logo tg3p + 4sen2p =3D +-r=
aiz de 11, dai como tg3p > 0 e sen2p > 0, n=F3s temos que : tg3pi/11 =
+ 4sen2pi/11 =3D raiz de 11</div>
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