0<\sin\alpha<1\\
\sin(\alpha+30)-?\\
30^0<\alpha+30^0<120^0==>0<\sin(\alpha+30^0)\leq1;\\
\sin(\alpha+30^0)=\sin\alpha\cos30^0+\cos\alpha\sin30^0=\\
=|\sin30^0=\frac12; \cos30^0=\frac{\sqrt3}{2}; \cos\alpha=0,6;\\
\sin\alpha=\sqrt{1-\cos^2\alpha}=\sqrt{1-0,6^2}=\sqrt{1-0,36}=\sqrt{0,64}=0,8;|\\
=0,8\frac{\sqrt3}{2}+0,6\frac12=0,4\sqrt3+0,3;\\
\sin(\alpha+30^0)=\frac{4\sqrt3+3}{10}" alt="\cos\alpha=0,6;\\
0<\alpha<90^0;==>0<\sin\alpha<1\\
\sin(\alpha+30)-?\\
30^0<\alpha+30^0<120^0==>0<\sin(\alpha+30^0)\leq1;\\
\sin(\alpha+30^0)=\sin\alpha\cos30^0+\cos\alpha\sin30^0=\\
=|\sin30^0=\frac12; \cos30^0=\frac{\sqrt3}{2}; \cos\alpha=0,6;\\
\sin\alpha=\sqrt{1-\cos^2\alpha}=\sqrt{1-0,6^2}=\sqrt{1-0,36}=\sqrt{0,64}=0,8;|\\
=0,8\frac{\sqrt3}{2}+0,6\frac12=0,4\sqrt3+0,3;\\
\sin(\alpha+30^0)=\frac{4\sqrt3+3}{10}" align="absmiddle" class="latex-formula">