\(tana.cota=1\Rightarrow tana=\dfrac{1}{cota}=\dfrac{1}{\dfrac{40}{9}}=\dfrac{9}{40}\)
\(1+tan^2a=\dfrac{1}{cos^2a}=1+\left(\dfrac{9}{40}\right)^2=\dfrac{1681}{1600}\\ \Rightarrow cos^2a=\dfrac{1600}{1681}\\ \Rightarrow cosa=\dfrac{40}{41}\)
\(1+cot^2a=\dfrac{1}{sin^2a}=1+\left(\dfrac{40}{9}\right)^2=\dfrac{1681}{81}\\ \Rightarrow sin^2a=\dfrac{81}{1681}\\ \Rightarrow sina=\dfrac{9}{41}\)
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