svp veuillez m'aider a faire ce petit exercice merci ;) On considère  un angle aigu. En utilisant les formules trigonométriques,démontre les égalités suivantes. a. 1+ tan²Â = 1/cos²Â b.1+ 1/ tan²Â = 1/sin²Â c. cos²Â- sin²  = 1- 2sin²Â d. (cos  + sin Â)² = 1+ 2sin  cos Â
Bonsoir,
a)[tex]1+\tan ^2 \widehat{A} = 1+\frac{\sin ^2 \widehat{A}}{\cos ^2\widehat{A}} = \frac{\cos ^2\widehat{A}+\sin ^2 \widehat{A}}{\cos ^2\widehat{A}} = \frac{1}{\cos ^2\widehat{A}}[/tex]
b)[tex]1+\frac{1}{\tan ^2 \widehat{A}} = 1+\frac{1}{\frac{\sin ^2\widehat{A}}{\cos ^2 \widehat{A}}} = 1+\frac{\cos ^2 \widehat{A}}{\sin ^2 \widehat{A}} = \frac{\sin^2\widehat{A}+\cos ^2 \widehat{A}}{\sin ^2 \widehat{A}} = \frac{1}{\sin^2 \widehat{A}}[/tex]
c)[tex]\cos ^2 \widehat{A} +\sin ^2 \widehat{A} = 1\\ \cos ^2 \widehat{A} +\sin ^2 \widehat{A} -2\sin ^2 \widehat{A}= 1-2\sin^2 \widehat{A}\\ \cos ^2 \widehat{A} -\sin ^2 \widehat{A} = 1-2\sin^2 \widehat{A}[/tex]
d)[tex]\left(\sin \widehat{A} + \cos \widehat{A}\right)^2\\ = \sin^2 \widehat{A} +\sin ^2 \widehat{A} +2\sin \widehat{A}\cos \widehat{A} \\ = 1+2\sin \widehat{A}\cos \widehat{A} [/tex]
