The equation you provided is:

$\text{tan}(90^\circ - A) = \frac{4}{3}$

Using the identity for the tangent of a complementary angle:

$\text{tan}(90^\circ - A) = \text{cot}(A)$

This gives us:

$\text{cot}(A) = \frac{4}{3}$

Since $\text{cot}(A) = \frac{1}{\text{tan}(A)}$, we can find $\text{tan}(A)$:

$\text{tan}(A) = \frac{3}{4}$

Thus, the solution to the equation is that $\text{tan}(A) = \frac{3}{4}$.

Would you like to go over any further steps or additional concepts?

Here are some related questions you might find helpful:

1. What is the relationship between cotangent and tangent functions?
2. How do you convert a cotangent to a tangent?
3. Can you derive other trigonometric values from $\text{tan}(A) = \frac{3}{4}$?
4. How do complementary angle identities work in trigonometry?
5. How does the unit circle help in understanding trigonometric identities?

Tip: Always remember that complementary angles add up to 90°, which is why $\text{tan}(90^\circ - A) = \text{cot}(A)$.