Una identidad trigonométricas, es una igualdad que se cumple para cualquier valor del ángulo que aparece en ella, medido indistintamente en grados o radianes. Se han clasificado en los siguientes grupos:
1. Identidades fundamentales
1.1 ![sen^{2}(x)+cos^{2}(x)=1](https://latex.codecogs.com/png.image?\dpi{110}&space;sen^{2}(x)+cos^{2}(x)=1)
1.2 ![sec^{2}(x)=1+tg^{2}(x)](https://latex.codecogs.com/png.image?\dpi{110}&space;sec^{2}(x)=1+tg^{2}(x))
1.3 ![csc^{2}(x)=1+ctg^{2}(x)](https://latex.codecogs.com/png.image?\dpi{110}&space;csc^{2}(x)=1+ctg^{2}(x))
1.4 ![Tg(x)=\frac{Sen(x)}{Cos(x)}](https://latex.codecogs.com/png.image?\dpi{110}&space;Tg(x)=\frac{Sen(x)}{Cos(x)})
1.5 ![Csc(x)=\frac{1}{Sen(x)}](https://latex.codecogs.com/png.image?\dpi{110}&space;Csc(x)=\frac{1}{Sen(x)})
1.6 ![Sec(x)=\frac{1}{Cos(x)}](https://latex.codecogs.com/png.image?\dpi{110}&space;Sec(x)=\frac{1}{Cos(x)})
1.7 ![Ctg(x)=\frac{Cos(x)}{Sen(x)}](https://latex.codecogs.com/png.image?\dpi{110}&space;Ctg(x)=\frac{Cos(x)}{Sen(x)})
2. Propiedades de suma y diferencia de ángulos
2.1 ![Sen(x+y)=Sen(x)*Cos(y)+Cos(x)*Sen(y)](https://latex.codecogs.com/png.image?\dpi{110}&space;Sen(x+y)=Sen(x)*Cos(y)+Cos(x)*Sen(y))
2.2 ![Sen(x-y)=Sen(x)*Cos(y)-Cos(x)*Sen(y)](https://latex.codecogs.com/png.image?\dpi{110}&space;Sen(x-y)=Sen(x)*Cos(y)-Cos(x)*Sen(y))
2.3 ![Cos(x+y)=Cos(x)*Cos(y)-Sen(x)*Sen(y)](https://latex.codecogs.com/png.image?\dpi{110}&space;Cos(x+y)=Cos(x)*Cos(y)-Sen(x)*Sen(y))
2.4 ![Cos(x-y)=Cos(x)*Cos(y)+Sen(x)*Sen(y)](https://latex.codecogs.com/png.image?\dpi{110}&space;Cos(x-y)=Cos(x)*Cos(y)+Sen(x)*Sen(y))
2.5 ![Tg(x+y)=\frac{Tg(x)+Tg(y)}{1-Tg(x)*Tg(y)}](https://latex.codecogs.com/png.image?\dpi{110}&space;Tg(x+y)=\frac{Tg(x)+Tg(y)}{1-Tg(x)*Tg(y)})
2.6 ![Tg(x-y)=\frac{Tg(x)-Tg(y)}{1+Tg(x)*Tg(y)}](https://latex.codecogs.com/svg.image?Tg(x-y)=\frac{Tg(x)-Tg(y)}{1+Tg(x)*Tg(y)})
3. Identidades de ángulo doble
3.1 ![Sen(2x)=2Sen(x)*Cos(x)](https://latex.codecogs.com/svg.image?Sen(2x)=2Sen(x)*Cos(x))
3.2 ![Cos(2x)=Cos^{2}(x)-Sen^{2}(x)](https://latex.codecogs.com/svg.image?Cos(2x)=Cos^{2}(x)-Sen^{2}(x))
3.3 ![Tg(2x)=\frac{2Tg(x)}{1-Tg^{2}(x)}](https://latex.codecogs.com/svg.image?Tg(2x)=\frac{2Tg(x)}{1-Tg^{2}(x)})
4. Identidades de ángulos negativos
4.1 ![Sen(-x)=-Sen(x)](https://latex.codecogs.com/svg.image?Sen(-x)=-Sen(x))
4.2 ![Csc(-x)=-Csc(x)](https://latex.codecogs.com/svg.image?Csc(-x)=-Csc(x))
4.3 ![Cos(-x)=Cos(x)](https://latex.codecogs.com/svg.image?Cos(-x)=Cos(x))
4.4 ![Sec(-x)=Sec(x)](https://latex.codecogs.com/svg.image?Sec(-x)=Sec(x))
4.5 ![Tg(-x)=-Tg(x)](https://latex.codecogs.com/svg.image?Tg(-x)=-Tg(x))
4.6 ![Ctg(-x)=-Ctg(x)](https://latex.codecogs.com/svg.image?Ctg(-x)=-Ctg(x))
5. Identidades del ángulo medio
5.1 ![Sen^{2}(\frac{x}{2})=\frac{1-Cos(x)}{2}\Rightarrow Sen(\frac{x}{2})= \pm \sqrt{\frac{1-Cos(x)}{2}}](https://latex.codecogs.com/svg.image?Sen^{2}(\frac{x}{2})=\frac{1-Cos(x)}{2}\Rightarrow&space;Sen(\frac{x}{2})=&space;\pm&space;\sqrt{\frac{1-Cos(x)}{2}})
5.2 ![Cos^{2}(\frac{x}{2})=\frac{1+Cos(x)}{2}\Rightarrow Cos(\frac{x}{2})= \pm \sqrt{\frac{1+Cos(x)}{2}}](https://latex.codecogs.com/svg.image?Cos^{2}(\frac{x}{2})=\frac{1+Cos(x)}{2}\Rightarrow&space;Cos(\frac{x}{2})=&space;\pm&space;\sqrt{\frac{1+Cos(x)}{2}})
5.3 ![Tg^{2}(\frac{x}{2})=\frac{1-Cos(x)}{1+Cos(x)}\Rightarrow Tg\left ( \frac{x}{2} \right )=\pm \sqrt{\frac{1-Cos(x)}{1+Cos(x)}}](https://latex.codecogs.com/svg.image?Tg^{2}(\frac{x}{2})=\frac{1-Cos(x)}{1+Cos(x)}\Rightarrow&space;Tg\left&space;(&space;\frac{x}{2}&space;\right&space;)=\pm&space;\sqrt{\frac{1-Cos(x)}{1+Cos(x)}})
6. Identidades del Cos(2x)
6.1 ![Sen^{2}(x)=\frac{1-Cos(2x)}{2}\Rightarrow Sen\left ( x \right )=\pm \sqrt{\frac{1-Cos(2x)}{2}}](https://latex.codecogs.com/svg.image?Sen^{2}(x)=\frac{1-Cos(2x)}{2}\Rightarrow&space;Sen\left&space;(&space;x&space;\right&space;)=\pm&space;\sqrt{\frac{1-Cos(2x)}{2}})
6.2 ![Cos^{2}(x)=\frac{1+Cos(2x)}{2}\Rightarrow Cos\left ( x \right )=\pm \sqrt{\frac{1+Cos(2x)}{2}}](https://latex.codecogs.com/svg.image?Cos^{2}(x)=\frac{1+Cos(2x)}{2}\Rightarrow&space;Cos\left&space;(&space;x&space;\right&space;)=\pm&space;\sqrt{\frac{1+Cos(2x)}{2}})
6.3 ![Tg^{2}(x)=\frac{1-Cos(2x)}{1+Cos(2x)}\Rightarrow Tg\left ( x \right )=\pm \sqrt{\frac{1-Cos(2x)}{1+Cos(2x)}}](https://latex.codecogs.com/svg.image?Tg^{2}(x)=\frac{1-Cos(2x)}{1+Cos(2x)}\Rightarrow&space;Tg\left&space;(&space;x&space;\right&space;)=\pm&space;\sqrt{\frac{1-Cos(2x)}{1+Cos(2x)}})
7. Identidades con ángulos de la forma ![(\frac{\pi }{2}-x)](https://latex.codecogs.com/svg.image?(\frac{\pi&space;}{2}-x))
7.1 ![Sen(\frac{\pi }{2}-x)= Cos(x)](https://latex.codecogs.com/svg.image?Sen(\frac{\pi&space;}{2}-x)=&space;Cos(x))
7.2 ![Csc(\frac{\pi }{2}-x)= Sec(x)](https://latex.codecogs.com/svg.image?Csc(\frac{\pi&space;}{2}-x)=&space;Sec(x))
7.3 ![Cos(\frac{\pi }{2}-x)= Sen(x)](https://latex.codecogs.com/svg.image?Cos(\frac{\pi&space;}{2}-x)=&space;Sen(x))
7.4 ![Sec(\frac{\pi }{2}-x)= Csc(x)](https://latex.codecogs.com/svg.image?Sec(\frac{\pi&space;}{2}-x)=&space;Csc(x))
7.5 ![Tg(\frac{\pi }{2}-x)= Ctg(x)](https://latex.codecogs.com/svg.image?Tg(\frac{\pi&space;}{2}-x)=&space;Ctg(x))
7.6 ![Ctg(\frac{\pi }{2}-x)= Tg(x)](https://latex.codecogs.com/svg.image?Ctg(\frac{\pi&space;}{2}-x)=&space;Tg(x))
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