Answer:
D) [tex]-\frac{3}{5}[/tex]
Step-by-step explanation:
Given
[tex]tan\theta=-2,\:\frac{\pi}{2}<\theta<\pi\\cos(2\theta)=?[/tex]
Use identities
[tex]cos(2\theta)=\frac{1-tan^2\theta}{1+tan^2\theta}\\\\cos(2\theta)=\frac{1-(-2)^2}{1+(-2)^2}\\\\cos(2\theta)=\frac{1-4}{1+4}\\ \\cos(2\theta)=-\frac{3}{5}[/tex]
