和差角與倍半角公式

 和角與差角公式

正弦:

• $\sin ( A + B ) = \sin A \cos B + \sin B \cos A$
• $\sin ( A - B ) = \sin A \cos B - \sin B \cos A$

餘弦:

• $\cos ( A + B ) = \cos A \cos B - \sin A \sin B$
• $\cos ( A - B ) = \cos A \cos B + \sin A \sin B$

正切:

• $\tan ( A + B ) = \dfrac{\tan A + \tan B}{1 - \tan A \tan B}$
• $\tan ( A - B ) = \dfrac{\tan A - \tan B}{1 + \tan A \tan B}$

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二倍角公式

• $\sin 2 \theta = 2 \sin \theta \cos \theta$
• $\\cos 2 \theta = \cos^2 \theta - \sin^2 \theta = 1 - 2 \sin^2 \theta = 2 \cos^2 \theta - 1$

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半角公式

• $\sin^2 \dfrac{\theta}{2} = \dfrac{1 - \cos \theta}{2}$
• $\sin \dfrac{\theta}{2} = \pm\sqrt{\dfrac{1 - \cos \theta}{2}}$
• $\cos^2 \dfrac{\theta}{2} = \dfrac{1 + \cos \theta}{2}$
• $\cos \dfrac{\theta}{2} = \pm\sqrt{\dfrac{1 + \cos \theta}{2}}$
• $\tan \dfrac{\theta}{2} = \dfrac{\sin \theta}{1 + \cos \theta} = \dfrac{1 - \cos \theta}{\sin \theta} = \pm\sqrt{\dfrac{1 - \cos \theta}{1 + \cos \theta}}$

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三倍角公式

• $\cos 3 \theta = 4 \cos^3 \theta - 3 \cos \theta$
• $\sin 3 \theta = - 4 \sin^3 \theta + 3 \sin \theta$