To simplify this expression, we can use the trigonometric identities:
Substitute these identities into the equation:
2*(-sin(x)) + sin(x) = -1/2-2sin(x) + sin(x) = -1/2-sin(x) = -1/2sin(x) = 1/2
Therefore, x = pi/6 or x = 5pi/6.
To simplify this expression, we can use the trigonometric identities:
sin(pi+x) = sin(pi)cos(x) + cos(pi)sin(x) = 0cos(x) - 1sin(x) = -sin(x)cos(pi/2-x) = cos(pi/2)cos(x) + sin(pi/2)sin(x) = 0cos(x) + 1sin(x) = sin(x)Substitute these identities into the equation:
2*(-sin(x)) + sin(x) = -1/2
-2sin(x) + sin(x) = -1/2
-sin(x) = -1/2
sin(x) = 1/2
Therefore, x = pi/6 or x = 5pi/6.