trig identity help?

Question

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

Answer 1

You are trying to prove that:
1 - cos²x + cot²x - cos²x (cot²x) = 1

Start with:
1 - cos²x + cot²x - cos²x (cot²x)

Pull out a common cot²x from the last two terms:
1 - cos²x + cot²x(1 - cos²x)

The expression in the parentheses is equal to sin²x:
1 - cos²x + cot²x(sin²x)

And cot²x = 1/tan²x = cos²x / sin²x:
1 - cos²x + (cos²x/sin²x)(sin²x)

The sin²x terms cancel out:
1 - cos²x + cos²x

And the cos²x terms cancel out
1

QED

Answer 2

1-cos^2x + cot^2x-cos^2x(cot^2x)= 1
-cos^2x + cot^2x-cos^2x(cot^2x)= 0
-1 + cot^2x/cos^2x - cot^2x = 0
-1+ 1/sin^2x - cos^2x/sin^2x = 0
-1 + (1-cos^2x)/sin^2x = 0
-1 +sin^2x/sin^2x=0
-1+1 = 0
0=0