[tex]sinB=cosC=\frac{AC}{BC} \\ \\ sinC=cosB=\frac{AB}{BC} \\ \\ sinB\cdot cosC+sinC\cdot cosB= \\ \\ \frac{AC}{BC}\cdot\frac{AC}{BC}+\frac{AB}{BC}\cdot\frac{AB}{BC}= \\ \\ \frac{AC^2}{BC^2}+\frac{AB^2}{BC^2}= \\ \\ \frac{AB^2+AC^2}{BC^2}= \\ \\ \frac{BC^2}{BC^2}=1[/tex]
