Final answer:
The expression (tan(57 degrees) - tan(21 degrees)) / (1 + tan(57 degrees)tan(21 degrees)) simplifies to tan(36 degrees) using the tangent subtraction formula.
Step-by-step explanation:
To write the expression (tan(57 degrees) - tan(21 degrees)) / (1 + tan(57 degrees)tan(21 degrees)) as a single trigonometric function, we can use a trigonometric identity known as the tangent subtraction formula. This identity is given by:
tan(A - B) = (tan(A) - tan(B)) / (1 + tan(A)tan(B))
Comparing the given expression with the identity, we see that A = 57 degrees and B = 21 degrees. Plugging these values into the identity, we get:
tan(57 degrees - 21 degrees) = tan(36 degrees).
Therefore, the expression simplifies to tan(36 degrees), which is a single trigonometric function.