Sum of Secant and Tangent

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Theorem

$\displaystyle \sec x + \tan x = \frac {1 + \sin x} {\cos x}$

	$\displaystyle $	$\displaystyle $	$\displaystyle $	$\displaystyle \sec x + \tan x$	$=$	$\displaystyle \frac 1 {\cos x} + \frac {\sin x} {\cos x}$	$\displaystyle $	$\displaystyle $	$\displaystyle $	by definition of tangent and secant
	$\displaystyle $	$\displaystyle $	$\displaystyle $	$\displaystyle $	$=$	$\displaystyle \frac {1 + \sin x} {\cos x}$	$\displaystyle $	$\displaystyle $	$\displaystyle $

$\blacksquare$

	\(\displaystyle \)	\(\displaystyle \)	\(\displaystyle \)	\(\displaystyle \sec x + \tan x\)	\(=\)	\(\displaystyle \frac 1 {\cos x} + \frac {\sin x} {\cos x}\)	\(\displaystyle \)	\(\displaystyle \)	\(\displaystyle \)	by definition of tangent and secant
	\(\displaystyle \)	\(\displaystyle \)	\(\displaystyle \)	\(\displaystyle \)	\(=\)	\(\displaystyle \frac {1 + \sin x} {\cos x}\)	\(\displaystyle \)	\(\displaystyle \)	\(\displaystyle \)