If cos x=4/5, csc x <0 then
sin 2x=
cos 2x=
tan 2x=

If cos x = 4/5, we can deduce that the triangle that x is in is a triangle similar to a 3-4-5 right triangle (from the image attatched, we can see that angle x is C). Also, since csc x<0, we know that it is located in the 4th quadrant. Therefore, sin x = -3/5.

By the double angle identity, sin(2x) = 2*sin(x)*cos(x)=2*4/5*-3/5=-0.96

cos(2x) = 1-2sin(x)^2=1-2*(-3/5)^2=1-18/25=0.28

tan(2x)=sin(2x)/cos(2x)=24/7

I hope this was helpful.

the answer to this question is 3/19

step-by-step explanation: