Though I don't know much about math sybols in English, it's my answer to the exercise:

1,

tan(T)-cot(T)/ [tan(T)+cot(T)]

= sin^2(T)-cos^2(T)/ [sin^2(T)+cos^2(T)]

= sin^2(T)- cos^2(T) = 2sin^2(T) - 1

2,

1-cos(T)/sin(T)

= 1 - cos^2(T)/ [sin (T). (1+cos(T)]

= sin^2(T)/ [sin (T). (1+cos(T)]

= sin(T)/[1+cos(T)]

3,

1-tan^2(T)/1+tan^2(T)

= cos^2(T) - sin^2 (T)

= 1 - 2sin^2(T)