Question 34256
tan(x+y)=(TAN(X)+TAN(Y))/(1-TAN(X)*TAN(Y))
 if cscx=5/3=HYPOTENUSE/OPPOSITE SIDE....SO USING PYTHOGARUS 
ADJ.SIDE^2+OPP.SIDE^2=HYP.^2.....ADJ.^2+3^2=5^2...ADJ.^2=25-9=16
ADJ.SIDE=4....TAN(X)=OPP.SIDE/ADJ.SIDE=3/4
 and cosy=5/13 =ADJ.SIDE/HYP.
5^2+OPP.SIDE^2=13^2
OPP.SIDE^2=169-25=144
OPP.SIDE=12
TAN(Y)=OPP.SIDE/ADJ.SIDE=12/5
TAN(X+Y)=(3/4 + 12/5 )/(1 - (3/4)(12/5))
=(3*5+12*4)/(4*5-3*12)=(15+48)/(20-36)=-63/16