Question

Calcule A+B, sendo A= sen (pi+x).cos (pi+x) /sen (pi-x).cos (pi-x)

Answer 1

Simplificando A e B:

$A=\frac{sen(\pi+x)*cos(\pi+x)}{sen(\pi-x)*cos(pi-x)}=\\\\=\frac{(sen\;\pi*cos\;x+sen\;x*cos\;\pi)(cos\;\pi*cos\;x-sen\;\pi *sen\;x)}{(sen\;\pi*cos\;x-sen\;x*cos\;\pi)(cos\;\pi *cos\;x+sen\;\pi*sen\;x)}=\\\\=\frac{(-sen\;x)(-cos\;x)}{(sen\;x)(-cos\;x)}=-1\\\\B=\frac{sen(2\pi-x)-cos(2\pi-x)}{sen(\pi+x)+cos(\pi+x)}=\\\\=\frac{-sen\;x-cos\;x}{-sen\;x-cos\;x}=1$

$A+B=-1+1=0$