Question

lim ->0 1-cos^2 x/ 1- cos x

Answer 1

$\lim_{x \to 0} \frac{1-cos^2x}{1-cosx} \\ =\lim_{x \to 0} \frac{(1-cosx)(1+cosx)}{1-cosx} \\ =\lim_{x \to 0} 1+cosx=1+1=2$

Answer 2

lim x → 0 (1 - cos²x)/(1 - cos x)
lim x → 0 [(1 - cos x)(1 + cos x)/(1 -cos x)]
lim x → 0 (1 + cos x)
lim x → 0 (1 + cos x) = 1 + cos 0 = 1 + 1 = 2