[tex](sin \frac{a}{2} +cos \frac{a}{2} )^2=sin^2 \frac{a}{2} +2*sin \frac{a}{2} cos \frac{a}{2} +cos^2 \frac{a}{2} [/tex]
Stim ca [tex]sin^2x+cos^2x=1, [/tex] pentru orice x, deci
[tex]sin^2 \frac{a}{2} +cos^2 \frac{a}{2}=1 [/tex]
Stim ca sin 2x=2sinxcosx pt orice x, deci:
[tex]2*\sin \frac{a}{2} \cos \frac{a}{2}=\sin 2\frac{a}{2}=\sin a[/tex]
Inlocuim ce stim in prima egalitate si obtinem:
[tex]( \frac{7}{5} )^2=1+\sin a \\ \\ \sin a= 1-\frac{47}{25}= \frac{25}{25}-\frac{49}{25} \\ \\ \sin a=- \frac{24}{25} [/tex]
