(UnB) Trigonometria: Relações Trigonométricas Fundamentais
Enviado: 27 Jun 2008, 20:49
(UnB) Se [tex3]\tan \theta=a[/tex3] e [tex3]0 \leq \theta<\frac{\pi}{2},[/tex3] então [tex3]cos \theta=\frac{1}{\sqrt{1+a^2}}[/tex3] ?
[tex3]a\,=\,\Large\frac{\sqrt{1\,-\,\cos^2\theta}}{\cos\,\theta}\large\,\,\Longleftrightarrow\,\,a^2\cos^2\theta\,=\,1\,-\,\cos^2\theta\,\,\Longleftrightarrow\,\,\cos^2\theta(1\,+\,a^2)\,=\,1\,\,\Longleftrightarrow\,\,\cos \theta\,=\,\Large\frac{1}{\sqrt{1\,+\,a^2}}[/tex3]