Question

Podemos afirmar que sen 75 ° + cos 75 ° x tan75 ° é :


a) √2/6

b) √6 - √2/2

c) √3/2

d ) √6 + √2/2

Answer 1

Resposta:

item d)

Explicação passo-a-passo:

Lembretes: sen75=sen(30+45)=sen30.cos45+sen45.cos30

$sen30=\frac{1}{2}\\\\cos30=\frac{\sqrt{3}}{2}\\\\sen45=cos45=\frac{\sqrt{2}}{2}$

$sen75+cos75.tan75=sen75+cos75.\dfrac{sen75}{cos75}=sen75+sen75=2.sen75$

$2.sen75=2.sen(30+45)\\\\2.sen75=2.(sen30.cos45+sen45.cos30)\\\\2.sen75=2.(\dfrac{1}{2}.\dfrac{\sqrt{2}}{2}+\dfrac{\sqrt{2}}{2}.\dfrac{\sqrt{3}}{2})\\\\2.sen75=2.(\dfrac{\sqrt{2}}{4}+\dfrac{\sqrt{6}}{4})\\\\2.sen75=2.(\dfrac{\sqrt{2}+\sqrt{6}}{4})\\\\2.sen75=\dfrac{\sqrt{2}+\sqrt{6}}{2}$