เอกลักษณ์ตรีโกณมิติ

\sin \left(x+y\right)=\sin x \cos y + \cos x \sin y
\sin \left(x-y\right)=\sin x \cos y - \cos x \sin y
\cos \left(x+y\right)=\cos x \cos y - \sin x \sin y
\cos \left(x-y\right)=\cos x \cos y + \sin x \sin y
\sin x+\sin y=2\sin \left( \frac{x+y}{2} \right) \cos \left( \frac{x-y}{2} \right)
\sin x-\sin y=2\cos \left( \frac{x+y}{2} \right) \sin \left( \frac{x-y}{2} \right)
\cos x+\cos y=2\cos \left( \frac{x+y}{2} \right) \cos \left( \frac{x-y}{2} \right)
\cos x-\cos y=-2\sin \left( \frac{x+y}{2} \right)\sin \left( \frac{x-y}{2} \right)
\tan x+\tan y=\frac{\sin \left( x+y\right) }{\cos x\cos y}
\tan x-\tan y=\frac{\sin \left( x-y\right) }{\cos x\cos y}
\cot x+\cot y=\frac{\sin \left( x+y\right) }{\sin x\sin y}
\cot x-\cot y=\frac{-\sin \left( x-y\right) }{\sin x\sin y}

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