To solve the problem, let's use the trigonometric identities:

We know that:
\[
\tan A = \cot B
\]

The cotangent function is the reciprocal of the tangent function:
\[
\cot B = \frac{1}{\tan B}
\]

Thus:
\[
\tan A = \frac{1}{\tan B}
\]

The tangent and cotangent functions are related by the identity:
\[
\tan \theta = \cot (90^\circ - \theta)
\]

So:
\[
\tan A = \cot (90^\circ - A)
\]

Comparing this with:
\[
\tan A = \cot B
\]

We have:
\[
B = 90^\circ - A
\]

Adding \( A \) and \( B \):
\[
A + B = A + (90^\circ - A) = 90^\circ
\]

So, the correct answer is:

C. 90°