Please show your work Find sin2x cos2x and tan2x from the gi

Please show your work.

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) =

sec x = 6

hypotenuse = 6 , base = 1

perpendicular = sqrt ( 6^2 - 1 ) = sqrt 35

sin x = sqrt 35 /6 , cos x = 1 / 6

sin 2x = 2 sin x cos x

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

= sqrt 35 / 3 * 1/6

= - sqrt 35 / 18

cos (2x) = cos^2 x - sin^2 x

= 2 cos^2 x - 1

= 2 ( 1/36 ) - 1

= 1/18 -1

= 17 / 18

tan (2x ) = ( 2 tan x ) / ( 1- tan^2 x )

tan x = sqrt 35

tan ( 2x) = 2 sqrt 35 / 1 - 35

= - 2 sqrt 35 / 34