Answered

Proving Identities.
1.cos0+tan0=sin0
2.sin0+tan0/cot0+csc0=sin0tan0
3.sin0(1+cot^20)=csc0
4.(1-cos^20)(1+cot^20)=1
5.cos0/sec0-sin0/cot0=cos0cot0-tan0/csc0

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Charlenesillarviz
Sorry but I can only answer 1,3 and4.

1. cos + tan = sin
    cos + sin/cos = sin
             sin = sin

3. sin (1 + cot²) = csc
    sin (csc²)  =    csc
    sin ( 1/sin . csc) = csc
                   csc = csc

4.  ( 1 - cos²) (1 + cot²) = 1
       ( sin²)   (csc²)        = 1
          sin ² ( 1/ sin²)     = 1
                               1 = 1



:D  SMILE