I could really use help with these Trig Identities?

Question

please show me how to work these out? I was doing them incorrectly, apparently. You may only work on one side of the problem. I was working on both sides and now I'm very confused. Thank you so much 

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(1+sec^2Ɵ) / (1+tan^2Ɵ) = 1+cos^2Ɵ 

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(1) / (1-sinƟ) - (1) / (1+sinƟ) = 2secƟtanƟ 

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(1-cosƟ) / (sinƟ) + (sinƟ) / (1-cosƟ) = 2cscƟ 

Thank you for any step by step explanation or anything, really

Answer 1

1)

= R.H .S

L.H.S = R.H .S

2)

= R.H .S

L.H.S = R.H .S

Answer 2

continued ......

3)

    

   

              

= R.H .S

L.H.S = R.H .S