Cosine of Complement equals Sine/Proof 2

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Theorem

$\map \cos {\dfrac \pi 2 - \theta} = \sin \theta$


Proof

\(\displaystyle \cos \left({\frac \pi 2 - \theta}\right)\) \(=\) \(\displaystyle \cos \left({\theta - \frac \pi 2}\right)\) Cosine Function is Even
\(\displaystyle \) \(=\) \(\displaystyle \sin \left({\theta - \frac \pi 2 + \frac \pi 2}\right)\) Sine of Angle plus Right Angle
\(\displaystyle \) \(=\) \(\displaystyle \sin \theta\)

$\blacksquare$