Cosine in terms of Tangent

Theorem
Let $x$ be a real number such that $\cos x \ne 0$.

Then:

where $\sin$ denotes the real sine function and $\tan$ denotes the real tangent function.

Proof
Then from Sign of Cosine:

When $\cos x = 0$, $\tan x$ is undefined.

Also see

 * Trigonometric Functions in terms of each other