Explicație pas cu pas:
[tex]\sin^{2} (x) - \sin(x) = \cos^{2} (x) [/tex]
[tex]\sin^{2} (x) - \sin(x) = 1 - \sin^{2} (x)[/tex]
[tex]2\sin^{2} (x) - \sin(x) - 1 = 0[/tex]
[tex](2\sin(x) + 1)(\sin(x) - 1) = 0[/tex]
[tex]0 < x < \pi[/tex]
=>
[tex]2\sin(x) + 1 = 0 = > \sin(x) = - \frac{1}{2} \\ fara \: solutie[/tex]
[tex]\sin(x) - 1 = 0 = > \sin(x) = 1 \\ = > x = \frac{\pi}{2} [/tex]
