If you make a right triangle in quadrant 2 ( which is where you would be if x is between 90-180 degrees) and csc =3 opposite side =1 hypotenuse =3 and adjacent = sqroot 8
so sinx = 1/3 cosx= -sqroot8/3 and tan x= -1/sqroot 8
sin2x= 2sinxcosx= 2(1/3)(-sqroot8/3)= ( -2sqroot8)/9
cos2x = cos^2x-sin^2x= (-sqroot 8/3)^2 - (1/3)^2= 8/9-1/9= 7/9
tan 2x= 2tan a/1-tan^2 a = 2(-1/sqroot 8)/1-(-1/sqroot 8)^2=( -2/sqroot 8 )/(1-1/8) =
-2/sqroot 8/ ( 7/8)= (-16)/7sqroot8 = -16sqroot8/8= -2sqroot8
