Cosine is Reciprocal of Secant

Theorem

Let $\theta$ be an angle such that $\cos \theta \ne 0$.

Then:

$\cos \theta = \dfrac 1 {\sec \theta}$

where $\cos$ denotes the cosine function and $\sec$ denotes the secant function.

Proof

\(\ds \frac 1 {\cos \theta}\)

\(=\)

\(\ds \sec \theta\)

Secant is Reciprocal of Cosine

\(\ds \leadsto \ \ \)

\(\ds \cos \theta\)

\(=\)

\(\ds \frac 1 {\sec \theta}\)

$\sec \theta$ and $\dfrac 1 {\cos \theta}$ are not defined when $\cos \theta = 0$.

$\blacksquare$

Also see

• Trigonometric Functions in terms of each other