Find sin2x cos2x and tan2x from the given information secx

Find sin(2x), cos(2x), and tan(2x) from the given information. sec(x) = 6, x in Quadrant IV sin(2x) = cos(2x) = tan(2x) =

1) sec x = 6

cos x = 1/6

sin x = sqrt[1 – cos^2 x] = -sqrt(35)/6

tan x = sin x/cos x = -sqrt(35)

sin 2x = 2*sin x*cos x = 2*(-sqrt(35)/6)*(1/6) = -sqrt(35)/18

cos 2x = 2*cos^2 x – 1 = 2*(1/36) – 1 = -17/18

tan 2x = sin 2x/cos 2x = sqrt(35)/17

2) 2*cos 2x – 1 = 0

cos 2x = ½

2x = 60, 300

x = 30, 150 degree