1. **State the problem:** Simplify the expression $$\sin(90^\circ - \alpha) + \cos(90^\circ + \alpha) - \sin(180^\circ + \alpha)$$. 2. **Recall trigonometric identities:** - $$\sin(90^\circ - \alpha) = \cos(\alpha)$$ (co-function identity) - $$\cos(90^\circ + \alpha) = -\sin(\alpha)$$ (using $$\cos(90^\circ + x) = -\sin x$$) - $$\sin(180^\circ + \alpha) = -\sin(\alpha)$$ (using $$\sin(180^\circ + x) = -\sin x$$) 3. **Substitute the identities into the expression:** $$\cos(\alpha) + (-\sin(\alpha)) - (-\sin(\alpha))$$ 4. **Simplify the expression:** $$\cos(\alpha) - \sin(\alpha) + \sin(\alpha)$$ 5. **Cancel terms:** $$- \sin(\alpha) + \sin(\alpha) = 0$$ 6. **Final simplified result:** $$\cos(\alpha)$$ Therefore, the expression simplifies to $$\cos(\alpha)$$.