2sin x-(cos(x/2)+sin (x/2)=0

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To solve the given equation 2sin x - (cos(x/2) + sin(x/2) = 0, we can simplify it further by using trigonometric identities.

Recall the double angle formula for sin(2x):
sin(2x) = 2sin(x)cos(x)

Now, let's rewrite the given equation using the double angle formula:
2sin x - cos(x/2) - sin(x/2) = 0
2sin x - 2sin(x/2)cos(x/2) - sin(x/2) = 0
2sin x - 2sin(x/2)cos(x/2) - 2sin(x/2)cos(x/2) = 0
2sin x - 4sin(x/2)cos(x/2) = 0

Now, we can rewrite this in terms of sin(2x):
sin(2x) = 2sin xcos x

Therefore, the given equation simplifies to:
sin(2x) - 2sin(2x) = 0
-sin(2x) = 0

Since sin(2x) cannot be equal to 0, this implies that there are no solutions to the given equation.