Question

Prove que cos^2x+sen^2x=1

Answer 1

$sen~\theta=b/a\\a*sen~\theta=b\\\\cos~\theta=c/a\\a*cos~\theta=c$
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Aplicando o teorema de pitágoras no triângulo:

$a^{2}=b^{2}+c^{2}\\a^{2}=(a*sen~\theta)^{2}+(a*cos~\theta)^{2}\\a^{2}=a^{2}*sen^{2}\theta+a^{2}*cos^{2}\theta$

Colocando a² em evidência:

$a^{2}=a^{2}*(sen^{2}\theta+cos^{2}\theta)\\a^{2}/a^{2}=sen^{2}\theta+cos^{2}\theta\\\\\boxed{\boxed{sen^{2}\theta+cos^{2}\theta=1}}$