Precalculus, Chapter 5, 5.5, Section 5.5, Problem 22

By the double angle formulas
cos(2u)=2cos^2u-1,
sin(2u)=2sin(u)cos(u).
By the first formula cos(2u)=2*(-4/5)^2-1=7/25.
Because u is in the second quadrant, its sinus is positive and is equal to
sqrt(1-cos^2u)=3/5.
So by the second formula sin(2u)=2*3/5*(-4/5)=-24/25.
And tan(u)=sin(u)/cos(u)=-24/7.

The answer: sin(2u)=-24/25, cos(2u)=7/25, tan(2u)=-24/7.