Chapter 5 - Trigonometric Identities - Section 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 208: 17

$$(\sin\alpha-\cos\alpha)^2=1-2\sin\alpha\cos\alpha$$

$$A=(\sin\alpha-\cos\alpha)^2$$ $$A=\sin^2\alpha-2\sin\alpha\cos\alpha+\cos^2\alpha$$ $$A=(\sin^2\alpha+\cos^2\alpha)-2\sin\alpha\cos\alpha$$ - According to Pythagorean Identity: $$\sin^2\alpha+\cos^2\alpha=1$$ Therefore, $$A=1-2\sin\alpha\cos\alpha$$