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[SPAM] Re: [obm-l] trigonometria

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Subject: [SPAM] Re: [obm-l] trigonometria
From: Alvaro de Jesus Netto <alvaronetto@xxxxxxxxxxxx>
Date: Mon, 19 Nov 2007 23:07:52 -0300 (ART)
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Caro amigo.

(cosx)^2 + (cos2x)^2 + (cos3x)^2 = 1 <=>
(cosx)^2 + [(cosx)^2 -- (senx)^2]^2 + (cos3x)^2 = 1 <=>
(cosx)^2 + [(cosx)^4 + (senx)^4 -- 2.(senx)^2.(cosx)^2] + (cos3x)^2 = 1 <=>
(cosx)^2 + [(cosx)^4 + (senx)^4 + 2.(senx)^2.(cosx)^2 -- 4.(senx)^2.(cosx)^2] + (cos3x)^2 = 1 <=>
(cosx)^2 + [(cosx)^2 + (senx)^2]^2 -- 4.(senx)^2.(cosx)^2 + (cos3x)^2 = 1 <=>
(cosx)^2 + 1 -- 4.(senx)^2.(cosx)^2 + (cos3x)^2 = 1 <=>
(cosx)^2 -- 4.(senx)^2.(cosx)^2 + (cos3x)^2 = 0 <=>
(cosx)^2 + (cos3x)^2 = 4.(senx)^2.(cosx)^2 <=>
(cosx)^2 + (4.(cosx)^3 -- 3.cosx)^2 = 4.(senx)^2.(cosx)^2 <=>
(cosx)^2.{1 + [4.(cosx)^2 -- 3]^2}  = 4.(senx)^2.(cosx)^2 <=>
(cosx)^2 = 0 ou 1 + [4.(cosx)^2 -- 3]^2  = 4.(senx)^2 <=>
(cosx)^2 = 0 ou 1 + 16.(cosx)^4 + 9 -- 24.(cosx)^2  = 4.[1 -- (cosx)^2] <=>
(cosx)^2 = 0 ou 8.(cosx)^4 -- 10.(cosx)^2 + 3 = 0 <=>
(cosx)^2 = 0 ou (cosx)^2 = 3/4 ou (cosx)^2 = 1/2 <=>
cosx = 0 ou cosx = +-- sqrt(3)/2 ou cosx = +-- sqrt(2)/2 <=>
x = k.Pi + Pi/2 ou x = k.Pi +-- Pi/6 ou x = k.Pi +-- Pi/4 (k é inteiro).

Até a próxima. 


Alvaro de Jesus Netto.
 

       
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Caro amigo.<br><br>(cosx)^2 + (cos2x)^2 + (cos3x)^2 = 1 &lt;=&gt;<br>(cosx)^2 + [(cosx)^2 -- (senx)^2]^2 + (cos3x)^2 = 1 &lt;=&gt;<br>(cosx)^2 + [(cosx)^4 + (senx)^4 -- 2.(senx)^2.(cosx)^2] + (cos3x)^2 = 1 &lt;=&gt;<br>(cosx)^2 + [(cosx)^4 + (senx)^4 + 2.(senx)^2.(cosx)^2 -- 4.(senx)^2.(cosx)^2] + (cos3x)^2 = 1 &lt;=&gt;<br>(cosx)^2 + [(cosx)^2 + (senx)^2]^2 -- 4.(senx)^2.(cosx)^2 + (cos3x)^2 = 1 &lt;=&gt;<br>(cosx)^2 + 1 -- 4.(senx)^2.(cosx)^2 + (cos3x)^2 = 1 &lt;=&gt;<br>(cosx)^2 -- 4.(senx)^2.(cosx)^2 + (cos3x)^2 = 0 &lt;=&gt;<br>(cosx)^2 + (cos3x)^2 = 4.(senx)^2.(cosx)^2 &lt;=&gt;<br>(cosx)^2 + (4.(cosx)^3 -- 3.cosx)^2 = 4.(senx)^2.(cosx)^2 &lt;=&gt;<br>(cosx)^2.{1 + [4.(cosx)^2 -- 3]^2}&nbsp; = 4.(senx)^2.(cosx)^2 &lt;=&gt;<br>(cosx)^2 = 0 ou 1 + [4.(cosx)^2 -- 3]^2&nbsp; = 4.(senx)^2 &lt;=&gt;<br>(cosx)^2 = 0 ou 1 + 16.(cosx)^4 + 9 -- 24.(cosx)^2&nbsp; = 4.[1 -- (cosx)^2] &lt;=&gt;<br>(cosx)^2 = 0 ou 8.(cosx)^4 -- 10.(cosx)^2 + 3 = 0 &lt;=&gt;<br>(cosx)^2 = 0 ou
 (cosx)^2 = 3/4 ou (cosx)^2 = 1/2 &lt;=&gt;<br>cosx = 0 ou cosx = +-- sqrt(3)/2 ou cosx = +-- sqrt(2)/2 &lt;=&gt;<br>x = k.Pi + Pi/2 ou x = k.Pi +-- Pi/6 ou x = k.Pi +-- Pi/4 (k é inteiro).<br><br>Até a próxima. <BR><BR><P dir=ltr style="MARGIN-RIGHT: 0px" align=left><FONT face=arial color=#0000ff size=4>Alvaro de Jesus Netto.</FONT></P>
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References:
- [SPAM] [obm-l] trigonometria
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