Question

Please help me with these two questions I’m stuck.

Answer 1

1)

`\tan(2x) = (\sin(2x))/(\cos(2x)) = (2\sin(x)\cos(x))/(2cos^2(x)-1)`

`\sin^2(x)+\cos^2(x) =1 => \sin(x) = √(1-\cos^2(x)) = \sqrt{1-(25)/(169)} = \sqrt{(144)/(169)} = (12)/(13)`

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