Основные формулы тригонометрии

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Ответ:

Accepted Answer

\( \sin^2 \alpha + \cos^2 \alpha = 1 \)
\( \operatorname{tg} \alpha = \frac{\sin \alpha}{\cos \alpha} \)
\( \operatorname{ctg} \alpha = \frac{\cos \alpha}{\sin \alpha} \)
\( \operatorname{tg} \alpha \cdot \operatorname{ctg} \alpha = 1 \)
\( \sin(\alpha + \beta) = \sin \alpha \cos \beta + \sin \beta \cos \alpha \)
\( \cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta \)
\( \operatorname{tg}(\alpha + \beta) = \frac{\operatorname{tg} \alpha + \operatorname{tg} \beta}{1 - \operatorname{tg} \alpha \operatorname{tg} \beta} \)
\( \sin 2\alpha = 2 \sin \alpha \cos \alpha \)
\( \cos 2\alpha = \cos^2 \alpha - \sin^2 \alpha \)
\( \operatorname{tg} 2\alpha = \frac{2 \operatorname{tg} \alpha}{1 - \operatorname{tg}^2 \alpha} \)
\( 1 + \cos \alpha = 2 \cos^2 \frac{\alpha}{2} \)
\( 1 - \cos \alpha = 2 \sin^2 \frac{\alpha}{2} \)
\( \sin \alpha + \sin \beta = 2 \sin \frac{\alpha + \beta}{2} \cos \frac{\alpha - \beta}{2} \)
\( \sin \alpha - \sin \beta = 2 \sin \frac{\alpha - \beta}{2} \cos \frac{\alpha + \beta}{2} \)
\( \cos \alpha + \cos \beta = 2 \cos \frac{\alpha + \beta}{2} \cos \frac{\alpha - \beta}{2} \)
\( \cos \alpha - \cos \beta = -2 \sin \frac{\alpha + \beta}{2} \sin \frac{\alpha - \beta}{2} \)