Respuesta :
(2cosxsenx)
----------------------- =1+cosx+senx agrupo
cosx + senx -1
2cosxsenx
----------------------- =1+cosx+senx multiplico por la conjugada del denominador
(cosx+senx)-1
[(2cosxsenx)[(cosx+senx)+1]
------------------------------------------------- =1+cosx +senx factorizo denominador
[(cosx+senx)-1][(cosx +senx) +1]
(2cosxsenx)([cosx+senx)+1]
------------------------------------------ =1+cosx +senx aplico produc. notables en el denomi.
(cosx+senx)^2 -1
(2cosxsenx)[(cosx+senx)+1]
------------------------------------------ = 1+cosx+senx
cos^2(x) +2cosxsenx +sen^2(x)-1
(2cosxsenx)[(cosx+senx)+1
----------------------------------------- = 1+cosx+senx utilizo sen^2(x)+cos^2(x)=
cos^2x +2coxsenx +sen^2x-1
(2cosxsenx)[(cosx+senx)+1]
------------------------------------------- =1+cosx+senx
1+2cosxsenx-1
(2cosxsenx)[(cosx+senx)+1]
-------------------------------------------= 1+cosx+senx simplifico
2cosxsenx
cosx +senx+1=1+cosx+senx ordenando
1+cosx+senx =1+cosx+senx
----------------------- =1+cosx+senx agrupo
cosx + senx -1
2cosxsenx
----------------------- =1+cosx+senx multiplico por la conjugada del denominador
(cosx+senx)-1
[(2cosxsenx)[(cosx+senx)+1]
------------------------------------------------- =1+cosx +senx factorizo denominador
[(cosx+senx)-1][(cosx +senx) +1]
(2cosxsenx)([cosx+senx)+1]
------------------------------------------ =1+cosx +senx aplico produc. notables en el denomi.
(cosx+senx)^2 -1
(2cosxsenx)[(cosx+senx)+1]
------------------------------------------ = 1+cosx+senx
cos^2(x) +2cosxsenx +sen^2(x)-1
(2cosxsenx)[(cosx+senx)+1
----------------------------------------- = 1+cosx+senx utilizo sen^2(x)+cos^2(x)=
cos^2x +2coxsenx +sen^2x-1
(2cosxsenx)[(cosx+senx)+1]
------------------------------------------- =1+cosx+senx
1+2cosxsenx-1
(2cosxsenx)[(cosx+senx)+1]
-------------------------------------------= 1+cosx+senx simplifico
2cosxsenx
cosx +senx+1=1+cosx+senx ordenando
1+cosx+senx =1+cosx+senx