Question

Calcule:

Tg(45°-30°)=?

Answer 1

Lembre que tg (x / 2) = √(1 - cos x) / √(1 + cos x)
tg 15 = tg (30/2) = √(1 - cos 30) / √(1 + cos 30)

tg 15 = 2 - √3

Answer 2

 

Lembre-se qu$<var>sen (45-30)=sen 45.cos 30-sen30-.cos 45</var>$$<var>sen(45-30)=\frac{\sqrt2}{2}\cdot\frac{\sqrt3}{2}-\frac{1}{2}\cdot\frac{\sqrt2}{2}=\frac{\sqrt6}{4}-\frac{\sqrt2}{4}}=\frac{\sqrt6-\sqrt2}{4}</var>$e

 

 

Lembre-se que $<var>cos(45-30)=cos45\cdot cos30+sen45\cdot sen(30)</var>$ 

 

  $<var>tan(45-30)=\frac{\frac{\sqrt6-\sqrt2}{4}}{\frac{\sqrt6+\sqrt2}{4}}=\frac{\sqrt6-\sqrt2}{\sqrt6+\sqrt2}</var>$

 

 

Sabendo-se que $<var>tan a=\frac{sen a}{cos a}</var>$ 

temos

 

 $<var>tan(45-30)=\frac{\frac{\sqrt6-\sqrt2}{4}}{\frac{\sqrt6+\sqrt2}{4}}=\frac{\sqrt6-\sqrt2}{\sqrt6+\sqrt2}</var>$