sin alpha / cos alpha + cos alpha / sin alpha

To simplify this expression, we can combine the fractions by finding a common denominator:

= (sin alpha sin alpha + cos alpha cos alpha) / (cos alpha * sin alpha)

= (sin^2(alpha) + cos^2(alpha)) / (cos alpha * sin alpha)

Using the Pythagorean identity sin^2(alpha) + cos^2(alpha) = 1:

= 1 / (cos alpha * sin alpha)

Therefore, the simplified expression is 1 / (cos alpha * sin alpha).