Derivative of Sine Function/Proof 3

Theorem

$\map {\dfrac \d {\d x} } {\sin x} = \cos x$


Proof

\(\ds \dfrac \d {\d x} \sin x\) \(=\) \(\ds \dfrac \d {\d x} \map \cos {\frac \pi 2 - x}\) Cosine of Complement equals Sine
\(\ds \) \(=\) \(\ds \map \sin {\frac \pi 2 - x}\) Derivative of Cosine Function and Chain Rule for Derivatives
\(\ds \) \(=\) \(\ds \cos x\) Sine of Complement equals Cosine

$\blacksquare$

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