\(2,\\ b,\tan\alpha=2=\dfrac{\sin\alpha}{\cos\alpha}\Rightarrow\sin\alpha=2\cos\alpha\)
Mà \(\sin^2\alpha+\cos^2\alpha=1\)
\(\Leftrightarrow4\cos^2\alpha+\cos^2\alpha=1\\ \Leftrightarrow5\cos^2\alpha=1\\ \Leftrightarrow\cos^2\alpha=\dfrac{1}{5}\\ \Leftrightarrow\cos\alpha=\sqrt{\dfrac{1}{5}}=\dfrac{\sqrt{5}}{5}\\ \Leftrightarrow\sin\alpha=\dfrac{2\sqrt{5}}{5}\)
Bài 1:
\(\sin\widehat{C}=\dfrac{AH}{AC}=\dfrac{\sqrt{2}}{\sqrt{6}}=\dfrac{\sqrt{3}}{3}\)
\(\tan\widehat{B}=\dfrac{AH}{HB}=\dfrac{\sqrt{2}}{1}=\sqrt{2}\)
\(2,\\ a,\sin^2\alpha+\cos^2\alpha=1\\ \Leftrightarrow\sin\alpha=\sqrt{1-\cos^2\alpha}\\ \Leftrightarrow\sin\alpha=\sqrt{\dfrac{8}{9}}=\dfrac{2\sqrt{2}}{3}\\ \tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}=\dfrac{2\sqrt{2}}{3}:\dfrac{1}{3}=2\sqrt{2}\)
\(3,\\ a,\approx0,4115\\ b,\approx0,8454\\ c,\approx2,2045\\ d,\approx0,3105\)
