Power Reduction Formulas/Tangent Squared
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Theorem
- $\tan^2x = \dfrac {1 - \cos2x} {1 + \cos2x}$
where $\cos$ and $\tan$ denote cosine and tangent respectively.
Proof
\(\ds \tan^2 x\) | \(=\) | \(\ds \frac {\sin^2 x} {\cos^2 x}\) | Tangent is Sine divided by Cosine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {\frac {1 - \cos 2 x} 2} {\frac {\cos 2 x + 1} 2}\) | Square of Sine and Square of Cosine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {1 - \cos 2 x} {1 + \cos 2 x}\) | multiplying top and bottom by $2$ |
$\blacksquare$