Question

Știind că tg x=2/3 , să se calculeze tg(x + π/2) =?

Answer 1

$tg(x+\frac{\pi}{2})=sin(x+\pi/2 )/cos(x+\pi/2)\\\\=[sinxcos(\pi/2)+cosxsin(\pi/2)]/[cosxcos(\pi/2)-sinxsin(\pi/2)]\\\\=(0+cosx)/(0-sinx)\\\\=-cosx/sinx\\\\=-ctgx\\\\=-ctg(2/3)$