Question

sin^2 x / cos x - 1 as the limit approaches 0

Answer 1

Hint: sin^2 (x) = 1 - cos^2(x) = (1 - cos x)(1+cos x)
Now factor 1-cos x with the cos x - 1 in the denominator, and it cancels with a -1.
So you are really taking the limit of (1+cos x)/-1 = ?

Answer 2

As x-----> 0, (1+cos x) approaches 2.
So your answer is 2/-1 = -2.