Question

1. ((cosx)/(1 + sinx))+((1 + sinx)/(cosx))

2. ((cos(x)cot(x))/(1 - sin(x)))-1

Answer 1

1) (cos^2x+1+2sinx+sin^2x)/cosx(1+sinx)

= 2+2sinx/cosx(1+sinx)
= 2(1+sinx)/cosx(1+sinx)
= 2/cosx
= 2secx

i'm going to assume you know the identities i.e. cos^2x+sin^2x=1

2) (cosx x cosx/sinx)/-sinx
= cos^2x/sinx/sin^2x
= cos^2x/-sin^2x
= -cot^2x