To find the value of cos(135) - sin(45), we first need to determine the exact values of the cosine and sine functions at these angles.

We know that cos(135) is equal to -√2/2 and sin(45) is equal to √2/2.

Now, we can substitute these values into the expression:

cos(135) - sin(45) = -√2/2 - √2/2

Next, we simplify the expression by combining the terms:

-√2/2 - √2/2 = -2√2/2

Finally, we simplify further by dividing the numerator and denominator by 2 to get the final answer:

-2√2/2 = -√2

Therefore, cos(135) - sin(45) = -√2.