Corollary

Tag 0DOE, permanent. Cite it as [Bourbaki, Tag 0DOE].

Algebra, chapter IX, § 10. Angles

For every element $\theta$ of $O^+$ such that $t(\theta)$ is finite, one has

(7)

s(2\theta) = 2t(\theta)/(1 - \delta t(\theta)^2), \qquad c(2\theta) = (1 + \delta t(\theta)^2)/(1 - \delta t(\theta)^2).

For every element $\varphi$ of $S^+/H$ such that $t(\varphi)$ is finite and $1 + \delta t(\varphi)^2 \neq 0$ , one has (8)

t(2\varphi) = 2t(\varphi)/(1 + \delta t(\varphi)^2).

In fact this follows immediately from Prop. 6 and from the corollary to Prop. 3.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Nothing.