Use the Double-Angle Identity to find the exact value for cos 2x given sinx= square root of 2/4

Use the Double-Angle Identity to find the exact value for cos 2x given sinx= square root of 2/4

If sin x = sqrt(2) / 4, then sin^2 x = 2 / 16 = 1/8

Because cos 2x = 1 - 2 sin^2 x,

cos 2x = 1 - 2(1/8)
= 1 - 1/4
= 3/4

Is that sinx = √(2/4) or sinx = (√2)/4

For sin(x) = √2/4 = (√2)/4

cos(2x) = 1 - 2sin²x
. . . . . . = 1 - 2((√2)/4)²
. . . . . . = 1 - 2(2/16)
. . . . . . = 1 - 1/4
. . . . . . = 3/4

For sin(x) = √(2/4) = √(1/2)

cos(2x) = 1 - 2sin²x
. . . . . . = 1 - 2(√(1/2)²
. . . . . . = 1 - 2(1/2)
. . . . . . = 1 - 1
. . . . . . = 0

1 - cos(2x) = 2 *(sin(x))^2

cos(2x) = 1 - 2 *sqrt (2)/4 = 1-1/sqrt(2)

We found this without taking care about x itself as an angle or so on