Answer
Please refer to the step-by-step part below.
Work Step by Step
Use the identity $\sin(\alpha+\beta)=\sin(\alpha)\cos(\beta)+\cos(\alpha)\sin(\beta)$ to obtain:
$\sin(\frac{\pi}{2}+\theta)
\\=\sin(\frac{\pi}{2})\cos(\theta)+\sin(\theta)\cos(\frac{\pi}{2})
\\=1\cdot \cos(\theta)+0\cdot \sin(\theta)
\\=\cos(\theta)+0
\\=\cos{\theta}$
