Answer:
The value of tan(3π/4) is indeed -1.
Now, to evaluate tan(3π/4 - π), we can use the following trigonometric identity:
tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)*tan(b))
Applying this identity to the expression tan(3π/4 - π), we get:
tan(3π/4 - π) = (tan(3π/4) - tan(π)) / (1 + tan(3π/4)*tan(π))
Substituting the values of tan(3π/4) = -1 and tan(π) = 0, we get:
tan(3π/4 - π) = (-1 - 0) / (1 + (-1)*0) = -1
So the value of tan(3π/4 - π) is also -1, which is the same as the value of tan(3π/4).
In other words, the value of tan(3π/4 - π) is equal to the value of tan(3π/4) because π is equal to 180 degrees, which is a full rotation. Subtracting a full rotation from an angle simply results in an equivalent angle in the opposite direction. Thus, the values of tangent for both angles remain the same.