Answer:
[tex]\displaystyle \cos 2\theta=-\frac{7}{9}[/tex]
Step-by-step explanation:
Cosine Double Angle
Given the cosine of an angle θ, the cosine of 2θ is given by the formula:
[tex]\cos 2\theta=2\cos^2\theta-1[/tex]
Given
[tex]\displaystyle \cos \theta=\frac{1}{3}[/tex]
Calculate
[tex]\displaystyle \cos 2\theta=2\left(\frac{1}{3}\right)^2-1[/tex]
[tex]\displaystyle \cos 2\theta=2\left(\frac{1}{9}\right)-1[/tex]
[tex]\displaystyle \cos 2\theta=\frac{2}{9}-1=-\frac{7}{9}[/tex]
[tex]\mathbf{\displaystyle \cos 2\theta=-\frac{7}{9}}[/tex]
