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

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

Bonjour,

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

[tex][\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}[/tex]