Answer:
[tex]cos(2\theta)=-\frac{7}{25}[/tex]
Step-by-step explanation:
we are given
[tex]tan(\theta)=\frac{4}{3}[/tex]
Firstly, we will draw triangle
Since, angle lies in third quadrant
so,
[tex]sin(\theta)=-\frac{4}{5}[/tex]
[tex]cos(\theta)=-\frac{3}{5}[/tex]
now, we can sue formula
[tex]cos(2\theta)=cos^2(\theta)-sin^2(\theta)[/tex]
now, we can plug values
[tex]cos(2\theta)=(-\frac{3}{5})^2-(-\frac{4}{5})^2[/tex]
we can simplify it
[tex]cos(2\theta)=-\frac{7}{25}[/tex]
