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

2. $tan\theta =\frac{\sqrt{5}}{5}$ 일 때, $cos2\theta$의 값은?

 

$$cos2\theta =co{s}^2\theta -si{n}^2\theta =2co{s}^2\theta -1$$

$$ta{n}^2\theta =\frac{si{n}^2\theta }{co{s}^2\theta }=\frac{1-co{s}^2\theta }{co{s}^2\theta }$$

$$co{s}^2\theta =\frac{1}{1+ta{n}^2\theta }=\frac{5}{6}$$

$$\therefore cos2\theta =\frac{2}{3}$$