Question

Simplify (1+csc x)/cos x+cot x

Answer 1

(1 + cscx)/cosx+cotx = (1+cscx)/(cosx+cosx/sinx)
 = (1+cscx)/cosx(1+1/sinx)
 = (1+cscx)/cosx(1+cscx)
 = 1/cosx
 = secx

Answer 2

(1+cscx)/(cos x + cot x) 
As cosec x is the inverse of sinx 
csc x = 1/sinx,
and cotx is the ratio of cosx and sinx 
cotx = cosx/sinx
(1+cscx)/(cos x + cot x) 
(1 + 1/sinx) / (cosx + cosx/sinx)
BY taking LCM:
(sinx +1) / sinx* [ (sinxcosx + cosx) / sinx]
 (sinx + 1) / (sinxcosx + cosx)
Taking cosx as common: 
= (sinx + 1) / cosx*(sinx + 1) 
= 1/ cosx is the answer