Answer:
To find all solutions of the equation sin^2(x/2) + cos(x) - 1 = 0 in the interval [0, 27), we can use a graphing utility to graph the equation and determine the x-values where the graph intersects the x-axis. This will give us the solutions of the equation.
Using a graphing utility, we plot the function y = sin^2(x/2) + cos(x) - 1 and examine the x-values where the graph intersects the x-axis.
After graphing the equation, we find that the graph intersects the x-axis at x = 0, x = 4π, x = 6π, x = 8π, and x = 26π.
Since we are considering the interval [0, 27), we can discard the solutions x = 26π and x = 8π as they are outside the given interval.
Therefore, the solutions of the equation sin^2(x/2) + cos(x) - 1 = 0 in the interval [0, 27) are x = 0, x = 4π, and x = 6π.