Rearranging yields
sin^2(x) = 1/4sin2(x)=14.
sin(x) = +-1/2sin(x)=±12.
Now, we must simply find the solutions to this sine function.
We know that the sine of 30 degrees (pi/6π6 radians) satisfies the positive equality, so we can simply apply this to all 4 quadrants. For example, possible solutions include pi/6, (5pi)/6, (7pi)/6, (11pi)/6, (13pi)/6π6,5π6,7π6,11π6,13π6, so on and so forth. Thus, we can express our answer as {x|x in pi/6 + pik or (5pi)/6 + pik}{x∣x∈π6+πkor5π6+πk}, where k in ZZ. Simply put, there are an infinite number of solutions to this equation, and we must use an arbitrary variable k to denote this.
