Solve the equation.

Question

(Enter your answers as a comma-separated list. Use n as an arbitrary integer. Enter your response in radians.)

2 − 4 sin² x = 0

x =

Answer 1

2-4sin^2(x)=0

sin^2(x)=1/2

sinx =+/- 1/sqr2= +/-sqr2/2

x =pi/4 +2npi, 3pi/4 +2npi, 4pi/4+2npi, 7pi/4+2npi

Answer 2

Starting with the given equation:

2 - 4 sin^2(x) = 0

We can rearrange it to get:

sin^2(x) = 1/2

Taking the square root of both sides, we have:

sin(x) = ±√(1/2)

Using the unit circle, we know that the solutions for sin(x) = √(1/2) are π/4 + 2πn and 7π/4 + 2πn, where n is an arbitrary integer. Similarly, the solutions for sin(x) = -√(1/2) are 3π/4 + 2πn and 5π/4 + 2πn, where n is an arbitrary integer.

Therefore, the solutions for the equation 2 - 4 sin^2(x) = 0 are:

x = π/4 + 2πn, 3π/4 + 2πn, 5π/4 + 2πn, 7π/4 + 2πn

where n is an arbitrary integer, and the solutions are in radians.