Question

Se Tag (α) = 2, então Sen (2α) é igual a?

Answer 1

$Tg( \alpha ) = 2 \\ \\ \frac{sen( \alpha)}{cos( \alpha)} = 2 \\ \\ Cos( \alpha) = \frac{sen( \alpha)}{2} \\ \\ Sen(2 \alpha) = 2.sen( \alpha).cos( \alpha) \\ Sen(2 \alpha) = 2.sen( \alpha).\frac{sen( \alpha)}{2} \\ \\ Sen(2 \alpha) = sen^2( \alpha) \\ \\ \\ \\ sen^2( \alpha) + cos^2( \alpha) = 1 \\ \\ sen^2( \alpha) + ( \frac{sen( \alpha)}{2})^2 = 1 \\ \\ sen^2( \alpha) + \frac{sen^2( \alpha)}{4} = 1 \\ \\ \frac{5sen^2( \alpha)}{4} = 1 \\ \\ sen^2( \alpha) = \frac{4}{5}$

Answer 2

Boa noite 

tg(α) = 2

sen(2α) = 2sen(α)*cos(α) 

sen(α) = tg(α)/√[1 + tg²(α)]
sen(α) = 2/√[1 + 4] = 2√5/5 

cos(α) =  1/√[1 + tg²(α)]
cos(α) =  1/√[1 + 4] = √5/5 

sen(2α) = 2sen(α)*cos(α)
sen(2α) = 2"2√5/5*√5/5 = 4/5