1)
[tex]\tan(2x) = \frac{\sin(2x)}{\cos(2x)} = \frac{2\sin(x)\cos(x)}{2cos^2(x)-1}[/tex]
[tex]\sin^2(x)+\cos^2(x) =1 => \sin(x) = \sqrt{1-\cos^2(x)} = \sqrt{1-\frac{25}{169}} = \sqrt{\frac{144}{169}} = \frac{12}{13}[/tex]
Meaning 2sin(x)cos(x) = 2 * 12/13 * 5 / 13 = 120/169.
2cos^2(x) - 1 = (2 * 25/169) - 1 = (50 - 169)/169 = -119/169 =>
(2sin(x)cos(x))/(2cos^2(x) -1) = [120/169]/[-119/169] = -120/119
2)
tan(x/2) = 3
