\(tan \theta = \frac{\sqrt{5}}{5} \) 일 때, \( cos 2 \theta \)의 값은?

2. \(tan \theta = \frac{\sqrt{5}}{5} \) 일 때, \( cos 2 \theta \)의 값은?

 

\[ cos 2 \theta = cos^2 \theta - sin^2 \theta = 2cos^2 \theta - 1\]

\[ tan^2 \theta = \frac{sin^2 \theta}{cos^2 \theta} = \frac{1-cos^2 \theta}{cos^2 \theta} \]

\[ cos^2 \theta = \frac{ 1 }{1+tan^2 \theta} = \frac{5}{6} \]

\[ \therefore cos 2 \theta = \frac{2}{3} \]