Posted by Lindsay on Monday, July 16, 2012 at 12:42am.
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