\(0< a< \dfrac{\pi}{2}\Rightarrow cosa>0\)
\(\Rightarrow cosa=\sqrt{1-sin^2a}=\dfrac{2\sqrt{2}}{3}\)
\(sin\left(a-\dfrac{\pi}{4}\right)=sina.cos\left(\dfrac{\pi}{4}\right)-cosa.sin\left(\dfrac{\pi}{4}\right)=\dfrac{1}{3}.\dfrac{\sqrt{2}}{2}-\dfrac{2\sqrt{2}}{3}.\dfrac{\sqrt{2}}{2}=\dfrac{\sqrt{2}-8}{6}\)
\(cos\left(a-\dfrac{\pi}{6}\right)=cosa.cos\left(\dfrac{\pi}{6}\right)+sina.sin\left(\dfrac{\pi}{6}\right)=\dfrac{2\sqrt{2}}{3}.\dfrac{1}{2}+\dfrac{1}{3}.\dfrac{1}{2}=\dfrac{2\sqrt{2}+1}{6}\)
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