Question

Resolver o calculo de trigonometria:

y= 1+tg(π/12) 

      1-tg(π/12)

Answer 1

Observemos que:

 

$\alpha (\circ)=\alpha (\text{rad})\cdot\dfrac{\pi}{180^{\circ}}$

 

Desta maneira, temos:

 

$\dfrac{\pi}{12}=\dfrac{\pi}{12}\cdot\dfrac{180}{\pi}=15^{\circ}$

 

Então, podemos afirmar que:

 

$\text{y}=\dfrac{1+\text{tg}~15^{\circ}}{1-\text{tg}~15^{\circ}}$

 

Como $\text{tg}~15^{\circ}=2-\sqrt{3}$, obtemos:

 

$\text{y}=\dfrac{1+(2-\sqrt{3})}{1-(2-\sqrt{3})}$

 

$\text{y}=\dfrac{3-\sqrt{3}}{-1+\sqrt{3}}$

 

Donde, temos:

 

$\text{y}=\dfrac{3+3\sqrt{3}-\sqrt{3}-3}{1-3}$

 

$\text{y}=\dfrac{-2\sqrt{3}}{-2}$

 

$\text{y}=\sqrt{3}$