Secant Minus Cosine
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Theorem
- $\sec x - \cos x = \sin x \tan x$
Proof
| \(\ds \sec x - \cos x\) | \(=\) | \(\ds \frac 1 {\cos x} - \cos x\) | Secant is Reciprocal of Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {1 - \cos^2 x} {\cos x}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {\sin^2 x} {\cos x}\) | Sum of Squares of Sine and Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sin x \tan x\) | Tangent is Sine divided by Cosine |
$\blacksquare$