Derivative of Sine Function/Proof 3
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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 |
$\blacksquare$