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Δ₉₀°ABC
[tex]\frac{sinB+cosC}{sinC+cosB} = ctgC[/tex]
[tex]---- // ----[/tex]
[tex]\frac{\frac{AC}{BC}+\frac{AC}{BC} }{\frac{AB}{BC}+\frac{AB}{BC} } = \frac{\frac{2AC}{BC} }{\frac{2AB}{BC} } =\frac{2AC}{BC} *\frac{BC}{2AB} =\frac{AC}{AB}[/tex] [tex](1)[/tex]
[tex]ctgC=\frac{AC}{AB}[/tex] [tex](2)[/tex]
[tex](1)=(2) =>[/tex] [tex]\frac{sinB+cosC}{sinC+cosB} = ctgC[/tex] [tex]{\mathbf{(A)}}[/tex]
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