SOLUTION: Solve the equation Sin x + sin 3x= sin2x + sin4x

Question 858714: Solve the equation Sin x + sin 3x= sin2x + sin4x
Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
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
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