I'm only aloud to manipulate one side of the problem and the end result has to match the other side of the equation

Question

Problem 1. sinx + cosx + sinx + tanx + cosxcotx = secx + cscx

Problem 2. ((sinx + cosx)/(1 + tanx))^2 + ((sinx - cos^2x)/(1 - cotx))^2 = 1

Problem 3. ((1 + sinx)/cosx) + (cosx/(1 + sinx)) = 2secx

Answer 1

I did the first one, after fixing your typo

http://www.jiskha.com/display.cgi?id=1351823844

Answer 2

#2 does not work for x=30° so there is a typo, or it is not and identity.

#3
LS = (1+sinx)/cosx + cosx/(1+sinx)
using LCD of cosx(1+sinx)

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