seno, coseno y tangente sin utilizar calculadora I

$$\begin{gathered} \sin 15º = \sin \left(45º-30º\right)=\sin 45º·\cos 30º-\cos 45º·\sin 30º\Rightarrow \\ \sin 15º =\frac{\sqrt{2}}{2}·\frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}·\frac{1}{2}\Rightarrow \\ \boxed{\sin 15º=\frac{\left(\sqrt{3}-1\right)\sqrt{2}}{4}} \end{gathered}$$

$$\begin{gathered} \cos 15º=\cos \left(45º-30º\right)=\cos 45º· \cos 30º + \sin 45º ·\hspace{0.17em}\sin 30º\Rightarrow \\ \cos 15º=\frac{\sqrt{2}}{2}·\frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}·\frac{1}{2}\Rightarrow \\ \boxed{\cos 15º=\frac{\left(\sqrt{3}+1\right)\sqrt{2}}{4}} \end{gathered}$$

$$\begin{gathered} \text{tg} 15º=\text{tg}\left(45º-30º\right)=\frac{\text{tg} 45º-\text{ tg} 30º}{1+\text{tg} 45º·\text{tg} 30º}\Rightarrow \\ \text{tg} 15º=\frac{1-{\displaystyle \frac{\sqrt{3}}{3}}}{1+{\displaystyle \frac{\sqrt{3}}{3}}}= \\ \boxed{\text{tg} 15º = \frac{3-\sqrt{3}}{3+\sqrt{3}}} \end{gathered}$$