Chapter 5 - Trigonometric Identities - Section 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 218: 3

$E$. $\sin x$

Use the Cosine of a Difference formula: $\cos(x+y)=\cos x \cos y -\sin x \sin y$ $\cos \left(\frac{ \pi}{2}-x\right)=\cos \frac{\pi}{2}\cos x+\sin\frac{\pi}{2} \sin x=0\times\cos x+1\times \sin x=\sin x$ The expression $3$ in Column I matches the expression $E$ in Column II.