Răspuns:
[tex]sin(x)=\frac{1}{2}+cos(x)=>sin(x)-cos(x)=\frac{1}{2} |*()^2[/tex]
[tex]sin^2(x)+cos^2(x)-2sin(x)*cos(x)=\frac{1}{4}[/tex]
[tex]1-2sin(x)*cos(x)=\frac{1}{4}[/tex]
[tex]-2sin(x)*cos(x)=\frac{1}{4}-1[/tex]
[tex]-2sin(x)*cos(x)=-\frac{3}{4}|*(-1)[/tex]
[tex]2sin(x)*cos(x)=\frac{3}{4}[/tex]
[tex]sin(2x)=\frac{3}{4}[/tex]
