ThmDex – An index of mathematical definitions, results, and conjectures.
Fundamental theorem of real trigonometry
Formulation 0
Let $\sin$ be the D1931: Standard real sine function.
Let $\cos$ be the D1927: Standard real cosine function.
Let $x \in \mathbb{R}$ be a D993: Real number.
Then \begin{equation} \sin^2 x + \cos^2 x = 1 \end{equation}
Proofs
Proof 0
Let $\sin$ be the D1931: Standard real sine function.
Let $\cos$ be the D1927: Standard real cosine function.
Let $x \in \mathbb{R}$ be a D993: Real number.
This result is a particular case of R5126: Fundamental theorem of complex trigonometry. $\square$