sin^2t / (1 + cos t) + cos t = 1

To simplify this expression, we can first substitute sin^2t = 1 - cos^2t:

(1 - cos^2t) / (1 + cos t) + cos t = 1

Next, we can combine the two fractions:

(1 - cos^2t + cos t(1 + cos t)) / (1 + cos t) = 1

Now we can distribute cos t:

(1 - cos^2t + cos t + cos^2t) / (1 + cos t) = 1

Simplify further by combining like terms in the numerator:

(1 + cos t) / (1 + cos t) = 1

We are left with:

1 = 1

Therefore, the given expression is true for all values of t.