1-Cos^2x = Sin^2x and Sinx = 1/Cscx so sin^2x = 1/ Csc^2x

AND 1+ Cot^2x = Csc^2x

Now:

[1/Csc^2x]* Csc^2x = Csc^2x/Csc^2x = 1

1=1

(1-cos^2 x)(1+cot^2 x)= 1

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

(a+cot^2x)=csc^2x

(sin^2x)(csc^2x)=1

cscx=1/sinx

csc^2x=1/sin^2x

(sin^2x)(1/sin^2x)=1

(sin^2x/sin^2x)=1

1=1