Sum of Secant and Tangent

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

\(\ds \)

\(=\)

\(\ds \frac {1 + \sin x} {\cos x}\)

$\blacksquare$

Also see

• One Plus Tangent Half Angle over One Minus Tangent Half Angle