hi vaibhav....ur question is
in a triangle ABC,D,E are the points on B,C suchthat BD=DE=EC IF

BAD=
X

DAE=Y

EAC=Z SHOW THAT SIN{X+Y}SIN{Y+Z}/SINXSINZ=4
This is a easy one ..u have to just understand wat is given
the solution is
consider angle BDA = q and angle BEA= w
from triangle BAE,
2a/sin(x+y) = c/sinw.............(1)
from triangle BAD,
a/3sinx=c/sinq .............(2)
now,eqn.(2)/(1)
a/sinx.3sin(x+y)/2a =
c/sinq .sin(w)/c
sin(x+y)/2sinx=sinw/sinq ...........(3)
from triangle DAC,
2a/3sin(y+z)=b/sinq
from triangle EAC,
a/3sinz=b/sinw
sin(y+z)/2sinz=sinq/sinw.......(4)
therefore,from (3)X(4) we get
sin(x+y)sin(y+z)/sinxsinz = 4