trigonometric sum of angles formulas like sin(x+y)=sin(x)*cos(y)+sin(y)*cos(x)
are identities in that for any x and y that are real numbers the equation are always true
but to make clear the equations are super important for angle sums we also call them formulas.
use them for your problem and when you see trig sum formulas, those are two of them.
Important note sin(x)=-√(1-(8/17)2)=[-√(172-82)]/17 note also sin(x) in fourth quadrant is negative (sin(A)=+/-√(1-cos2(A)) another definition/identity).
similarly cos(y)=[-√(252-242)]/25 where cos(y) in second quadrant is negative.
tan(A)=sin(A)/cos(A) is a definition and therefore an identity, so tan(x)=(-√(172-82)(17*8/17)=(-√(172-82))/8
be careful with all the algebra