Ta có \(\tan B=\cot C=0,75=\frac{3}{4}\)
\(\Rightarrow\tan C=1:\cot C=1:\frac{3}{4}=\frac{4}{3}\)
Lại có: \(\cot C=\frac{\cos C}{\sin C}\Leftrightarrow\frac{\cos C}{\sin C}=\frac{3}{4}\Leftrightarrow\cos C=\frac{3}{4}\sin C\)
Mặt khác:
\(\sin^2C+\cos^2C=1\Leftrightarrow\sin^2C+\left(\frac{3}{4}\sin C\right)^2=1\\ \Leftrightarrow\sin^2C+\frac{9}{16}\sin^2C=1\\ \Leftrightarrow\frac{25}{16}\sin^2C=1\\ \Leftrightarrow\sin^2C=1:\frac{25}{16}=\frac{16}{25}\\ \Leftrightarrow\sin C=\frac{4}{5}\)
Suy ra \(\cos C=\frac{3}{4}\sin C=\frac{3}{4}\cdot\frac{4}{5}=\frac{3}{5}\)
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