Bonsoir,
Convention d'écriture : (tan Â)² = tan² Â (valable aussi avec sin et cos).
[tex]1+\tan ^2 \widehat{A} = 1+\frac{\sin^2 \widehat{A}}{\cos ^2 \widehat{A}} = \frac{\sin^2 \widehat{A}+\cos^2\widehat{A}}{\cos^2 \widehat{A}} = \frac{1}{\cos^2 \widehat{A}}[/tex]
On applique la formule :
[tex]1+\tan^2 \widehat{A} = \frac{1}{\cos^2 \widehat{A}}\\ +1^2 = \frac{1}{\cos^2 \widehat{A}}\\ 2 = \frac{1}{\cos^2 \widehat{A}}\\ \cos^2 \widehat{A} = \frac 12\\ \cos \widehat{A} = \frac{1}{\sqrt 2} = \frac{\sqrt 2}{2}\\[/tex]
