How do you find the solutions of the equation 2sin^2 (x) = 1

Solve for x:

2 sin^2 (x) = 1

Divide both sides by 2:

sin^2 (x) = 1/2

Take the square root of both sides:

sin (x) = 1/sqrt (2) or sin (x) = - 1/sqrt (2)

Take the inverse sine of both sides:

x = 2 π n_1 + (3 π) / 4 for n_1 element Z or x = 2 π n_2 + π/4 for n_2 element Z or sin (x) = - 1/sqrt (2)

Take the inverse sine of both sides:

Answer: x = 2 π n_1 + (3 π) / 4 for n_1 element Z or x = 2 π n_2 + π/4 for n_2 element Z or x = 2 π n_3 + (5 π) / 4 for n_3 element Z or x = 2 π n_4 + (7 π) / 4 for n_4 element Z