Question

Fie a,b nr.reale astfel incat  sin a + cos b=1 si cos a + sin b=1/2.Calculati sin(a+b)

Answer 1

Ridicam la patrat cele doua egalitati.
[tex](sina+cosb)^2=1^2=>sin^2a+2sina\cdot cosb+cos^2b=1[1]\\ (cosa+sinb)^2= (\frac{1}{2})^2=>cos^2a+2cos\ \cdot sinb+sin^2b= \frac{1}{4}[2]\\ Adunam \ [1]+[2]=> 1+2sin(a+b)+1= \frac{5}{4} \\ 2sin(a+b)= \frac{5}{4} -2\\ 2sin(a+b)= -\frac{3}{4} \\ sin(a+b)= -\frac{3}{8} \\[/tex]