cot^2(X) + cos^2(X)+sin^2(X)= csc^2(X)

My answer that I keep coming up with is cos^2(x), not its reciprical. What am I doing wrong?

cot^2 = 1/tan^2

tan = sin/cos

therefore, 1/tan = cos/sin

cot^2 = cos^2/sin^2

also

csc = 1/sin

so csc^2 = 1/sin^2

with those identities...

cos^2/sin^2 + cos^2 + sin^2 = 1/sin^2

multiply all by sin^2

cos^2 + cos^2sin^2 + sin^4 = 1

"undistribute" the sin^2

sin^2(sin^2 + cos^2) + cos^2 = 1

I'm sure you can take it from here.