1. We start with the given formula: $$\cos(2t) = 1 - 2\sin^2(t)$$ 2. This is a double-angle identity for cosine, which relates the cosine of twice an angle to the sine squared of the angle. 3. The formula can be rearranged to express $\sin^2(t)$ in terms of $\cos(2t)$: $$\cos(2t) = 1 - 2\sin^2(t)$$ Subtract 1 from both sides: $$\cos(2t) - 1 = -2\sin^2(t)$$ 4. Divide both sides by $-2$ to isolate $\sin^2(t)$: $$\sin^2(t) = \frac{\cancel{\cos(2t) - 1}}{\cancel{-2}} = \frac{1 - \cos(2t)}{2}$$ 5. This is a useful identity to express $\sin^2(t)$ in terms of $\cos(2t)$: $$\sin^2(t) = \frac{1 - \cos(2t)}{2}$$ 6. This formula is often used in trigonometry to simplify expressions involving $\sin^2(t)$ or to solve equations. Final answer: $$\sin^2(t) = \frac{1 - \cos(2t)}{2}$$