To solve this equation, we can use the double angle identity for sine, which states that sin(2θ) = 2sinθcosθ.

Given that sin(π/4) = √2/2 and cos(π/4) = √2/2, we can rewrite the equation as:

2(sin(π/4)cos(π/4) - sin(π/4)cos(x)) = √2
2(√2/2 √2/2 - √2/2 cos(x)) = √2
2(1/2 - √2/2 * cos(x)) = √2

Simplifying further, we get:

1 - √2 cos(x) = 1
√2 cos(x) = 0
cos(x) = 0

Therefore, x must be a multiple of π/2, such as x = 0, π/2, π, 3π/2, etc.