Final answer:
To simplify the expression (2 sint cost) dt, we can rewrite it as sin(2t) dt.
Step-by-step explanation:
To simplify the expression (2 sint cost) dt, we can use the trigonometric identities. From the given trigonometric identities, we know that sin(α ± β) = sin α cos β ± cos α sin β. Applying this identity, we have 2 sin t cos t, which can be rewritten as sin(2t). So, the expression is equivalent to sin(2t) dt.