Question

Sa se afle sin a stiind ca :

Answer 1

$(sin \frac{a}{2} +cos \frac{a}{2} )^2=sin^2 \frac{a}{2} +2*sin \frac{a}{2} cos \frac{a}{2} +cos^2 \frac{a}{2}$

Stim ca $sin^2x+cos^2x=1,$ pentru orice x, deci 
$sin^2 \frac{a}{2} +cos^2 \frac{a}{2}=1$

Stim ca sin 2x=2sinxcosx pt orice x, deci:
$2*\sin \frac{a}{2} \cos \frac{a}{2}=\sin 2\frac{a}{2}=\sin a$ 

Inlocuim ce stim in prima egalitate si obtinem:
$( \frac{7}{5} )^2=1+\sin a \\ \\ \sin a= 1-\frac{47}{25}= \frac{25}{25}-\frac{49}{25} \\ \\ \sin a=- \frac{24}{25}$