Trigonometry
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10 grade
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39 Terms
\sin^2 \alpha + \cos^2 \alpha
1
\tan \alpha
\frac{\sin \alpha}{\cos \alpha}
\cot \alpha
\frac{\cos \alpha}{\sin \alpha}
\tan \alpha \cdot \cot \alpha
1
1 + \tan^2 \alpha
\frac{1}{\cos^2 \alpha}
1 + \cot^2 \alpha
\frac{1}{\sin^2 \alpha}
\sin(\alpha \pm \beta)
\sin \alpha \cos \beta \pm \cos \alpha \sin \beta
\cos(\alpha \pm \beta)
\cos \alpha \cos \beta \mp \sin \alpha \sin \beta
\tan(\alpha \pm \beta)
\frac{\tan \alpha \pm \tan \beta}{1 \mp \tan \alpha \tan \beta}
\cot(\alpha \pm \beta)
\frac{\cot \alpha \cot \beta \mp 1}{\cot \beta \pm \cot \alpha}
\sin 2\alpha
2\sin \alpha \cos \alpha
\cos 2\alpha
\cos^2 \alpha - \sin^2 \alpha
\tan 2\alpha
\frac{2\tan \alpha}{1 - \tan^2 \alpha}
\cot 2\alpha
\frac{\cot^2 \alpha - 1}{2\cot \alpha}
\sin 3\alpha
3\sin \alpha - 4\sin^3 \alpha
\cos 3\alpha
4\cos^3 \alpha - 3\cos \alpha
\tan 3\alpha
\frac{3\tan \alpha - \tan^3 \alpha}{1 - 3\tan^2 \alpha}
\cot 3\alpha
\frac{3\cot \alpha - \cot^3 \alpha}{1 - 3\cot^2 \alpha}
\sin^2 \alpha
\frac{1 - \cos 2\alpha}{2}
\cos^2 \alpha
\frac{1 + \cos 2\alpha}{2}
\sin \alpha \sin \beta
\frac{1}{2}(\cos(\alpha - \beta) - \cos(\alpha + \beta))
\cos \alpha \cos \beta
\frac{1}{2}(\cos(\alpha - \beta) + \cos(\alpha + \beta))
\sin \alpha \cos \beta
\frac{1}{2}(\sin(\alpha - \beta) + \sin(\alpha + \beta))
\sin \frac{\alpha}{2}
\pm\sqrt{\frac{1 - \cos \alpha}{2}}
\cos \frac{\alpha}{2}
\pm\sqrt{\frac{1 + \cos \alpha}{2}}
\tan \frac{\alpha}{2}
\pm\sqrt{\frac{1 - \cos \alpha}{1 + \cos \alpha}} = \frac{\sin \alpha}{1 + \cos \alpha} = \frac{1 - \cos \alpha}{\sin \alpha}
\cot \frac{\alpha}{2}
\pm\sqrt{\frac{1 + \cos \alpha}{1 - \cos \alpha}} = \frac{\sin \alpha}{1 - \cos \alpha} = \frac{1 + \cos \alpha}{\sin \alpha}
\sin \alpha \text{ (через } \tan \frac{\alpha}{2})
\frac{2\tan \frac{\alpha}{2}}{1 + \tan^2 \frac{\alpha}{2}}
\cos \alpha \text{ (через } \tan \frac{\alpha}{2})
\frac{1 - \tan^2 \frac{\alpha}{2}}{1 + \tan^2 \frac{\alpha}{2}}
\tan \alpha \text{ (через } \tan \frac{\alpha}{2})
\frac{2\tan \frac{\alpha}{2}}{1 - \tan^2 \frac{\alpha}{2}}
\cot \alpha \text{ (через } \tan \frac{\alpha}{2})
\frac{1 - \tan^2 \frac{\alpha}{2}}{2\tan \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}
\tan \alpha + \tan \beta
\frac{\sin(\alpha + \beta)}{\cos \alpha \cos \beta}
\tan \alpha - \tan \beta
\frac{\sin(\alpha - \beta)}{\cos \alpha \cos \beta}
\cot \alpha + \cot \beta
\frac{\sin(\alpha + \beta)}{\sin \alpha \sin \beta}
\cot \alpha - \cot \beta
\frac{\sin(\alpha-\beta)}{\sin\alpha\sin\beta}
