To solve the equation √2(cosx - sinx) = 1, we first need to isolate the trigonometric function. We can start by dividing both sides by √2:

cosx - sinx = 1/√2

Next, we can rewrite sinx as cos(π/2 - x) using the cosine addition formula:

cosx - cos(π/2 - x) = 1/√2

Now, we can apply the cosine subtraction formula to simplify the equation:

cos(x - π/4) = 1/√2

Now, we have cos(x - π/4) = cos(π/4), which implies that the argument inside the cosine function is equivalent to each other:

x - π/4 = π/4 + 2πn OR x - π/4 = -π/4 + 2πn

Solve for x:

x = π/2 + 2πn OR x = 0 + 2πn

So the general solution to the equation cosx - sinx = 1/√2 is x = π/2 + 2πn or x = 2πn, where n is an integer.