Основное тригонометрическое тождество

$$\sin^2\alpha+\cos^2\alpha=1$$  

$$\sin^2\alpha-\cos^2\alpha=1$$  

$$1+\sin^2\alpha=\cos^2\alpha$$  

$$\sin^2\alpha\times\cos^2\alpha=1$$  

$$\sin\alpha=\pm\sqrt[]{1-\cos^2\alpha}$$  

$$\sin\alpha=\pm\sqrt[]{1+\cos^2\alpha}$$  

$$\sin\alpha=\pm\sqrt[]{\cos^2\alpha-1}$$  

$$\sin\alpha=\sqrt[]{1+\cos^2\alpha}$$  

$$\cos\alpha=\pm\sqrt[]{1-\sin^2\alpha}$$  

$$\cos\alpha=\sqrt[]{1-\sin^2\alpha}$$  

$$\cos\alpha=\pm\sqrt[]{1+\sin^2\alpha}$$  

$$\cos\alpha=\pm\sqrt[]{2-\sin^2\alpha}$$  

$$tg\ \alpha\times\operatorname{ctg}\alpha=1$$  

$$tg\alpha+\operatorname{ctg}\alpha=1$$  

$$\operatorname{ctg}\alpha\times tg\alpha=2$$  

$$tg\alpha\times\operatorname{ctg}\alpha=3$$  

$$tg\alpha=\frac{\sin\alpha}{\cos\alpha}$$  

$$tg\alpha=\frac{\cos\alpha}{\sin\alpha}$$  

$$tg\alpha=\sin\alpha\times\cos\alpha$$  

$$tg\alpha=\frac{1}{\operatorname{ctg}\alpha}$$  

$$\operatorname{ctg}\alpha=\frac{\cos\alpha}{\sin\alpha}$$  

$$\operatorname{ctg}\alpha=\frac{1}{tg\alpha}$$  

$$\operatorname{ctg}\alpha=\frac{\sin\alpha}{\cos\alpha}$$  

$$\operatorname{ctg}\alpha=\frac{1}{\sin\alpha}$$  

$$tg^2\alpha+1=\frac{1}{\cos^2\alpha}$$  

$$tg^2\alpha-1=\frac{1}{\cos^2\alpha}$$  

$$tg^2\alpha+1=\frac{1}{\cos^{ }\alpha}$$  

$$tg^{ }\alpha+1=\frac{1}{\cos^2\alpha}$$  

$$tg\alpha=\frac{1}{\operatorname{ctg}\alpha}$$  

$$tg\alpha=\frac{1}{\operatorname{ctg}^2\alpha}$$  

$$tg\alpha=1+\operatorname{ctg}\alpha$$  

$$tg\alpha=\frac{2}{\operatorname{ctg}\alpha}$$  

$$\operatorname{ctg}\alpha=\frac{1}{tg\alpha}$$  

$$\operatorname{ctg}\alpha=1\times tg\alpha$$  

$$\operatorname{ctg}\alpha=1+tg\alpha$$  

$$\operatorname{ctg}\alpha=\frac{1}{2tg\alpha}$$  

$$\operatorname{ctg}^2\alpha+1=\frac{1}{\sin^2\alpha}$$  

$$\operatorname{ctg}^2\alpha-1=\frac{1}{\sin^2\alpha}$$  

$$\operatorname{ctg}^2\alpha+1=\frac{1}{\sin2\alpha}$$  

$$\operatorname{ctg}^2\alpha=\frac{1}{\sin^2\alpha}+1$$