Răspuns:
[tex]x[/tex]∈[tex](0;\frac{\pi }{2} ) => cos>0, sin>0, tan>0, ctg>0[/tex]
[tex]cosx=tg\frac{\pi }{3}*sinx[/tex]
[tex]cosx=\sqrt{3}*sinx[/tex]
[tex]cos^2x=3sin^2x[/tex]
Dupa formula fundamentala a trigonometriei:
[tex]sin^2x+cos^2x=1\\sin^2x+(3sin^2x)=1\\4sin^2x=1[/tex]
[tex]sin^2x=\frac{1}{4}|\sqrt{...}[/tex]
[tex]sinx=\frac{1}{2}[/tex]
