Question

Ayuda
(2cosxsenx)/(cosx+senx-1) = 1+cosx+senx

Answer 1

(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