Final answer:
To simplify (1+tan(t))/(1+cot(t)) to a single trigonometric function, use the identity tan(t) = 1/cot(t) and simplify the expression by multiplying the numerator and denominator by cot(t). The final simplified expression is cot(t) + 1/cot(t).
Step-by-step explanation:
To simplify the expression (1+tan(t))/(1+cot(t)) to a single trigonometric function, we can use the identity tan(t) = 1/cot(t). Substituting this into the expression, we get (1 + 1/cot(t))/(1 + cot(t)).
Next, we can simplify further by multiplying the numerator and denominator of the expression by cot(t). This gives us (cot(t) + 1)/(cot(t) + cot²(t)).
Finally, combining like terms, we can rewrite the expression as cot(t) + 1/cot(t).