Question

simplifique a expressão sen(pi-x)-cos(pi/2-x)/cos(2pi-x)

Answer 1

Abra as funções

$sin(\pi-x)=sin(\pi)*cos(x)+sin(x)*cos(\pi)=-sin(x)$

$cos\left(\frac{\pi}{2}-x\right)=cos\left(\frac{\pi}{2}\right)*cos(x)+sin\left(\frac{\pi}{2}\right)*sin(x)=sin(x)$

$cos\left(2\pi-x\right)=cos\left(2\pi\right)*cos(x)+sin\left(2\pi\right)*sin(x)=cos(x)$

dai ficamos com:

$sin(x)-\frac{sin(x)}{cos(x)}$

$\boxed{\boxed{sin(x)-tan(x)}}$