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Re: [obm-l] Trigonometria
- To: obm-l@xxxxxxxxxxxxxx
- Subject: Re: [obm-l] Trigonometria
- From: "Andre Araujo" <alsdearaujo@xxxxxxxxx>
- Date: Sat, 30 Jun 2007 12:58:37 -0300
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Raphael,
1/sen2x + 1/cos2x= 1+cotg2x + 1+tg2x => (sen2x + cos2x)/(sen2x * cos2x) = 2 + [sen^2 (2x) + cos^2 (2x)]/(sen2x * cos2x)
sen2x + cos2x = 1 + 2*(sen2x * cos2x) => sen^2 (2x) + cos^2 (2x) + 2* (sen2x * cos2x) = 1 + 4*[sen^2 (2x) * cos^2 (2x)] + 4*[sen(2x) * cos(2x)] => 4*[sen^2 (2x) * cos^2 (2x)] + 2*[sen(2x) * cos(2x)] => 2*(sen2x * cos2x) ( 2*sen2x * cos2x + 1) = 0
sen4x = -1 => 4x = 3*pi/2 + 2*k*pi, k inteiro. Assim, x = 3*pi/8 + k*pi/2.
André Araújo.