Answer:
C. tan B
Explanation:
In ∆ABC, if angle A is 45 degrees and angle C is also 45 degrees, then the triangle is an isosceles right triangle. In such a triangle, the legs (the sides opposite and adjacent to the 45-degree angles) are congruent.
Since the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle, and since these two sides are congruent in an isosceles right triangle, we have tan A = 1.
Therefore, the correct answer is C. tan B.