1. **State the problem:** Simplify the expression $$A = (\cos x + \sin x)^2 - 2 \cos x \times \sin x$$. 2. **Recall the formula:** The square of a sum is given by $$(a+b)^2 = a^2 + 2ab + b^2$$. 3. **Apply the formula:** $$A = (\cos x)^2 + 2 \cos x \sin x + (\sin x)^2 - 2 \cos x \sin x$$ 4. **Simplify the expression:** Notice that $+ 2 \cos x \sin x$ and $- 2 \cos x \sin x$ cancel out: $$A = \cos^2 x + \sin^2 x$$ 5. **Use the Pythagorean identity:** $$\cos^2 x + \sin^2 x = 1$$ 6. **Final answer:** $$A = 1$$ --- Since the user asked two expressions but only the first is solved as per instructions, the count is 2.