IDENTIDADES TRIGO + Y - ANGULOS

$sen\ \left(\alpha+\beta\right)=sen\alpha\ \cos\beta+sen\alpha\ \cos\beta$

$sen\ \left(\alpha+\beta\right)=\ sen\ \alpha\ \cos\beta+\cos\alpha\ sen\beta$

$\cos\ \left(\alpha+\beta\right)=\ \cos\alpha\cos\beta-sen\ \alpha\ sen\ \beta$

$\cos\ \left(\alpha+\beta\right)=\ \cos\alpha\ \cos\beta+sen\ \alpha\ sen\ \beta$

$sen\ \left(\alpha-\beta\right)=sen\ \alpha\ \cos\beta+\ \cos\ \alpha\ sen\ \beta$

$sen\ \left(\alpha-\beta\right)=sen\ \alpha\ \cos\beta-\ \cos\ \alpha\ sen\ \beta$

$\cos\ \left(\alpha-\beta\right)=\cos\alpha\ \cos\beta\ +\ sen\ \alpha\ sen\ \beta$

$\cos\ \left(\alpha-\beta\right)=\ sen\ \alpha\ \cos\beta\ +\cos\ \alpha\ sen\ \beta$

 $sen\ 180°\ \cos\ 45°-\cos\ 180°\ sen\ 45°$  

 $sen\ 120°\ \cos\ 15°\ +\ \cos\ 120°\ sen\ 15°$  

 $=\left(0\right)\left(\frac{\sqrt{2}}{2}\right)-\left(-1\right)\left(\frac{\sqrt{2}}{2}\right)=\frac{2\sqrt{2}}{2}=\sqrt{2}$  

 $=\left(0\right)\left(\frac{\sqrt{2}}{2}\right)-\left(-1\right)\left(\frac{\sqrt{2}}{2}\right)=\frac{\sqrt{2}}{2}$  

 $\cos\ 90°\ \cos\ 30°-\ sen\ 90°\ sen\ 30°$  

 $\cos\ 90°\ \cos\ 30°\ +\ sen\ 90°\ sen\ 30°$  

 $\cos\ 150°\ \cos\ 30°-\ sen\ 150°\ sen\ 30°$  

 $=\left(0\right)\left(\frac{\sqrt{3}}{2}\right)-\left(\frac{\sqrt{2}}{2}\right)\left(\frac{1}{2}\right)\ =\frac{\sqrt{2}}{4}$  

 $=\left(0\right)\left(\frac{\sqrt{3}}{2}\right)-\left(1\right)\left(\frac{1}{2}\right)\ =\frac{1}{2}$