Question

sen(x+π/4)=sen(π/4-x) ??????​

Answer 1

Resposta:

Explicação passo-a-passo:

Sen(a+b) = Sen(a).Cos(b)+Sen(b).Cos(a)

e

Sen(a-b) = Sen(a).Cos(b)-Sen(b).Cos(a)

Onde a=π/4  e b=x

$Sen(\frac{\pi}{4}+x)=Sen(\frac{\pi}{4}).Cos(x)+Sen(x).Cos(\frac{\pi}{4})\\\\Sen(\frac{\pi}{4}+x)=\frac{\sqrt{2}}{2}.Cos(x)+Sen(x).\frac{\sqrt{2}}{2}\\\\Sen(\frac{\pi}{4}+x)=\frac{\sqrt{2}}{2}.(Cos(x)+Sen(x))\\\\\\\\Sen(\frac{\pi}{4}-x)=Sen(\frac{\pi}{4}).Cos(x)-Sen(x).Cos(\frac{\pi}{4})\\\\Sen(\frac{\pi}{4}-x)=\frac{\sqrt{2}}{2}.Cos(x)-Sen(x).\frac{\sqrt{2}}{2}\\\\Sen(\frac{\pi}{4}-x)=\frac{\sqrt{2}}{2}.(Cos(x)-Sen(x))\\\\\\\\Sen(\frac{\pi}{4}+x)\neq Sen(\frac{\pi}{4}-x)$