cot^2t/csct=(1-sin^2t)/sint

L.H.S. cot^2(t)/cosec(t) { I am assuming its cosec(t), u might have misspelled it}

putting cot(t)=cos(t)/sin(t) and cosec(t)=1/sin(t)
we get
L.H.S.= [cos^2(t)/sin^2(t)]/[1/sin(t)]
= [cos^2(t)/sin^2(t)] * sin(t)
=cos^2(t)/sin(t)

R.H.S. =[1-sin^2(t)]/sin(t)

now we know sin^2(t)+cos^2(t)=1
therefore 1-sin^2(t)=cos^2(t). Putting this value in R.H.S. we get

= cos^2(t)/sin(t)=L.H.S.

I Hope it helped