Question

Sen (120°+45°)=?? Qual é o resultado. Ajudem me

Answer 1

Sabemos que:

$\boxed{\mathsf{sen(a+b)=sen~a\cdot cos~b+sen~b\cdot cos~a}}\\ \\ \\ \mathsf{sen(120\°+45\°)=sen~120\°\cdot cos~45\°+sen~45\°\cdot cos~120\°}\\ \\ \mathsf{sen(120\°+45\°)=\dfrac{\sqrt{3}}{2}\cdot \dfrac{\sqrt{2}}{2}+\dfrac{\sqrt{2}}{2}\cdot -\dfrac{1}{2}}\\ \\ \\ \mathsf{sen(165\°)=\dfrac{\sqrt{6}}{4}-\dfrac{\sqrt{2}}{4}}\\ \\ \\ \boxed{\mathsf{sen~165\°=\frac{\sqrt{6}-\sqrt{2}}{4}}}$