[tex]\displaystyle\\\sin x=\pm\sqrt{1-\cos^2x}\\\\\sin x=\pm\sqrt{1-\left(\frac{\sqrt{3} }{2}\right)^\b2}}\\\\\\\sin x=\pm\sqrt{1-\frac{3 }{4}}}\\\\\sin x=\pm\sqrt{\frac{1}{4}}}\\\\\boxed{\sin x=\frac{1}{2}}\\\\\text{cctd}\\\text{Am ales semnul + deoarece suntem in cadranul 1}[/tex]
x∈(0,π/2)=>x∈C1=>sinx>0;cosx>0 (1)
sin²x+cos²x=1=>sin²x=1-cos²x=1-(√3/2)²=1-3/4=(4-3)/4=1/4=>sinx=±√(1/4)=±1/2 (2)
Din (1) si (2)=>sinx=1/2