Démontrer que: [tan (a)]² +1 = 1/[cos (a)]².... Pergunta de ideia deFleurale

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April 2019 2 123 Report

Démontrer que: [tan (a)]² +1 = 1/[cos (a)]²

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starvanessa1 [tan (a)]² +1 =[sin²(a)/cos²(a)]+1
=sin²(a)+cos²(a)/cos²(a)
=1/cos²(a)

0 votes Thanks 0

Commentaires Bonjour,

On sait que $\tan(a)=\dfrac{\sin(a)}{\cos(a)}\\\\\ [\sin(a)]^2+[\cos(a)]^2=1$

$[\tan(a)]^2+1=[\dfrac{\sin(a)}{\cos(a)}]^2+1\\\\\ [\tan(a)]^2+1=\dfrac{[\sin(a)]^2}{[\cos(a)]^2}+1\\\\\ [\tan(a)]^2+1=\dfrac{[\sin(a)]^2}{[\cos(a)]^2}+\dfrac{[\cos(a)[^2}{[\cos(a)]^2}\\\\\ [\tan(a)]^2+1=\dfrac{[\sin(a)]^2+[\cos(a)]^2}{[\cos(a)]^2}\\\\\ [\tan(a)]^2+1=\dfrac{1}{[\cos(a)]^2}$

2 votes Thanks 1