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