To simplify the expression cos²x - (cot²x + 1) * sin²x, we can use the trigonometric identities cot²x = cos²x / sin²x and cos²x = 1 - sin²x.
Substitute cot²x = cos²x / sin²x and cos²x = 1 - sin²x into the expression:
cos²x - (cot²x + 1) sin²x = cos²x - (cos²x / sin²x + 1) sin²x
= cos²x - cos²x - sin²x= 0 - sin²x= -sin²x
Therefore, cos²x - (cot²x + 1) * sin²x simplifies to -sin²x.
To simplify the expression cos²x - (cot²x + 1) * sin²x, we can use the trigonometric identities cot²x = cos²x / sin²x and cos²x = 1 - sin²x.
Substitute cot²x = cos²x / sin²x and cos²x = 1 - sin²x into the expression:
cos²x - (cot²x + 1) sin²x = cos²x - (cos²x / sin²x + 1) sin²x
= cos²x - cos²x - sin²x
= 0 - sin²x
= -sin²x
Therefore, cos²x - (cot²x + 1) * sin²x simplifies to -sin²x.