# How do you prove sin(pi/2-theta) = cos theta ?

Use $\sin \left(a - b\right) = \sin a \cos b - \cos a \sin b$. Here, $a = \frac{\pi}{2} \mathmr{and} b = \theta . \sin \left(\frac{\pi}{2}\right) = 1 \mathmr{and} \cos \left(\frac{\pi}{2}\right) = 0$.
This way, you can prove all similar results, like, for example, $\sin \left(\pi - \theta\right) = \sin \theta$.