Question

Simplify the expression: 1 + cot(t) / (1 + tan(t))

A) 1
B) 0
C) tan(t)
D) cot(t)"

Answer 1

The expression 1 + cot(t) / (1 + tan(t)) simplifies to 1 by substituting cot(t) with 1/tan(t) and simplifying the resultant expression.

Step-by-step explanation:

The expression to simplify is 1 + cot(t) / (1 + tan(t)). To simplify this expression, we use trigonometric identities. Recall that cot(t) = 1/tan(t) and by substituting this into the original expression, we have:

1 + (1/tan(t)) / (1 + tan(t))

We can write this as a single fraction:

(1 · tan(t) + 1) / (tan(t) + 1)

Which simplifies to:

tan(t) / tan(t) = 1

Thus, the expression simplifies to 1, which corresponds to option A.