\(cot\alpha=\dfrac{40}{9}\Rightarrow tan\alpha=\dfrac{1}{cot\alpha}=\dfrac{1}{\dfrac{40}{9}}=\dfrac{9}{40}\)
+) \(\dfrac{1}{cos^2\alpha}=1+tan^2\alpha\)
\(\Leftrightarrow\dfrac{1}{cos^2\alpha}=1+\left(\dfrac{9}{40}\right)^2\\ \Rightarrow cos\alpha=\sqrt{1:\left(1+\left(\dfrac{9}{40}\right)^2\right)}=\dfrac{40}{41}\)
+) \(sin^2\alpha=1-cos^2\alpha\)
\(\Leftrightarrow sin\alpha=\sqrt{1-cos^2\alpha}=\sqrt{1-\left(\dfrac{40}{41}\right)^2}=\dfrac{9}{41}\)
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