Question

Dado que sen(a+b)= sena . cosb + senb.cosa, calcule o sen75

Answer 1

Explicação passo-a-passo:

$\sf sen~(30^{\circ}+45^{\circ})=sen~30^{\circ}\cdot cos~45^{\circ}+sen~45^{\circ}\cdot cos~30^{\circ}$

$\sf sen~75^{\circ}=\dfrac{1}{2}\cdot\dfrac{\sqrt{2}}{2}+\dfrac{\sqrt{2}}{2}\cdot\dfrac{\sqrt{3}}{2}$

$\sf sen~75^{\circ}=\dfrac{\sqrt{2}}{4}+\dfrac{\sqrt{6}}{4}$

$\sf sen~75^{\circ}=\dfrac{\sqrt{2}+\sqrt{6}}{4}$