To solve the equation sqrt(2)cos(x) - sin(x) = sqrt(3), we can manipulate the equation using trigonometric identities and properties.

Let's first note that sqrt(3) can be expressed as 2sin(60°) or 2cos(30°) using trigonometric angle values. Therefore, we can rewrite the equation as:

sqrt(2)cos(x) - sin(x) = 2sin(60°)

Then, we apply the angle addition formula for sine:

sqrt(2)cos(x) - sin(x) = 2sin(60°)
sqrt(2)cos(x) - sin(x) = 2 * sin(45° + 15°)
sqrt(2)cos(x) - sin(x) = 2(sin(45°)cos(15°) + cos(45°)sin(15°))

Using angle values from trigonometric ratios:
sqrt(2)cos(x) - sin(x) = 2(1/sqrt(2) sqrt(6)/4 + sqrt(2)/2 sqrt(6)/4)
sqrt(2)cos(x) - sin(x) = 2(sqrt(6)/8 + sqrt(12)/8)
sqrt(2)cos(x) - sin(x) = 2(sqrt(6) + sqrt(12)) / 8

Now we have the equation in terms of cos(x) and sin(x). To solve for x, we can use the double angle formula for cosine:

sqrt(2)cos(x) - sin(x) = 2(sqrt(6) + sqrt(12)) / 8
sqrt(2)cos(x) - sin(x) = (2sqrt(6) + 2sqrt(12)) / 8
sqrt(2)(2cos^2(x) - 1) - 2sin(x) = 2sqrt(6) + 2sqrt(12)
2(2cos^2(x) - 1) - 2sin(x) = 2sqrt(6) + 2sqrt(12)
4cos^2(x) - 2 - 2sin(x) = 2sqrt(6) + 2sqrt(12)
4cos^2(x) - 2(1 + sin(x)) = 2sqrt(6) + 2sqrt(12)

From here, we can try to find the solutions through using trigonometric identities and numerical approximations. Let me know if you need further assistance with this equation.