Verified answer

sen(180-x) = sen(180)cos(-x)+sen(-x)cos(180)

= sen (x)

pues sen(180)=0, cos(180)=-1, sen(-x)=-sen(x)

csc(y)=csc(180-x)= 1/sen(180-x) = 1/sen(x)

cot(y) = 1/tan(y) = 1/tan(180-x) =

(1+ tan(180)tan(x)) / (tan(180)-tan(x))= -1/tan(x)

pues tan(180)=0

sen(x)csc(y)+tan(x)cot(y) =

sen(x)/sen(x) - tan(x)/tan(x) = 1-1=0

Espero que te sea útil

Pues muy facil!!!

x+y=180

y=180-x

E = sen x. csc y + tg x . cotg y

reemplazando: "y" por "180-x", queda:

E = sen x.csc(180-x) + tg x .cotg (180-x)

pero sabemos q

csc(180-x) = csc x

cotg(180-x) = -tg x

entonces

E= sen x .csc x + tg x.(-cotgx)

E=1-1

E=0

x+y=180

y=180-x

E = sen x. csc y + tg x . cotg y

reemplazando: "y" por "180-x", queda:

E = senx.csc(180-x) + tg x .cotg (180-x)

pero sabemos q

csc(180-x) = sen x

cotg(180-x) = -tg x

entonces

E= sen x .csc x + tg x.(-cotgx)

E=1-1

E=0

E= 720

Saludos¡¡¡