Question

Solutions to the equation 2cos²(x/3) - 1 = 0 in radians.

A) x = π/2
B) x = π/4
C) x = π/6
D) x = π/3

Answer 1

The solutions to the equation 2cos²(x/3) - 1 = 0 are x = 3π/4 and x = -3π/4.

Step-by-step explanation:

To solve the equation 2cos²(x/3) - 1 = 0, we can start by isolating the cosine term:

2cos²(x/3) = 1

Next, we divide both sides of the equation by 2:

cos²(x/3) = 1/2

Now, take the square root of both sides:

cos(x/3) = ±√(1/2)

Since cosine is positive in the first and fourth quadrants, we can write:

x/3 = ±π/4

Multiplying both sides by 3, we get:

x = ±3π/4

Thus, the solutions to the equation 2cos²(x/3) - 1 = 0 in radian measure are:

A) x = 3π/4

B) x = -3π/4