<PRE><B>Question 858714</B>
Solve the equation Sin x + sin 3x= sin2x + sin4x
 we know sin C+ sin D=2sin(C+d)/2 cos (c-D)/2
applying this formula both side
2 sin (x+3x)/2 cos (x-3x)/2=2 sin (2x+4x)/2 cos (2x-4x)/2
sin 2x.cos x =sin 3x .cos x      cancelling cos x from both side  
sin 2x=sin 3x
sin 2x- sin3x =0  by using formula  sin C- sin D
2 cos (2x +3x)/2 sin 2x-3x)/2=0
 2 cos5x/2 , sin (-x)/2=0
-2 cos 5x/2 .sin x/2=0
therefor 
cos 5x/2=0   or   sin x/2=0
   5x/2=90 degree  or    x/2= o degree 
    x=90x2/5=36 degree   or  x=0 degree </PRE>