Answer:
Step-by-step explanation:
[tex]sin(2\theta)=2sin\theta~cos\theta\\\\cos(2\theta)=cos^2\theta-sin^2\theta\\\\cos\theta=\frac{24}{25}\\\\sin^2\theta+cos^2\theta=1~=>sin\theta=\pm\sqrt{1-cos^2\theta}\\\\we ~will~ use~ the ~minus~ sign~because~sin\theta~is~negative~in~IV~cuadrant\\sin\theta=-\sqrt{1-{(\frac{24}{25})}^2}=-\frac{7}{25}[/tex]
Now we cal calculate the quantities requested
[tex]sin(2\theta)=2sin\theta cos\theta=2(-\frac{7}{25})\frac{24}{25}=-\frac{336}{625}\\\\[/tex]
[tex]cos(2\theta)=cos^2\theta-sin^2\theta=(\frac{24}{25})^2-(-\frac{7}{25})^2=\frac{527}{625}[/tex]
[tex]tan(2\theta)=\frac{sin(2\theta)}{cos(2\theta)}=\frac{-\frac{336}{625}}{\frac{527}{625}}=-\frac{336}{527}[/tex]
