Question

si= ctg x= 1/4

calcule : tg(45+x)

Answer 1

Primero tenemos que: Ctgx=1/4=cosx/senx-->senx=4cosx Tan(45+x)=sen(45+x)/cos(45+x) =(senxcos45+Sen45cosx)/(cosxcos45-senxsen45) =$((Senx)( \sqrt{2}/2)+( \sqrt{2}/2)(cosx))/((cosx)( \sqrt{2}/2)-(senx)( \sqrt{2}/2)) \\ =( \sqrt{2}/2)(senx+cosx)/( \sqrt{2}/2)(cosx-senx)= \\ (senx+cosx)/(cosx-senx) \\ =(4cosx+cosx)/(cosx-4cosx) \\ =5cosx/-3cosx=-5/3$