## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Apply the sum formula: $\sin(A+B)=\sin(A)\cos(B)+\cos(A)\sin(B)$ In order to prove the given identity, we simplify the left-hand side $\text{LHS}$ as follows: $\text{LHS } =\sin(\dfrac{\pi}{2}+\theta) \\=\sin(\dfrac{\pi}{2})\cos(\theta)+\sin(\theta)\cos(\dfrac{\pi}{2}) \\=1\cdot \cos(\theta)+0\cdot \sin(\theta) \\=\cos(\theta)+0 \\=\cos{\theta} \\=\text{ RHS}$