Limits.....

Question

Lim _θ-->Π/2     cot θ - cos θ / cos³θ

Answer 1

lim_θ→Π/2 (cot θ - cos θ) / cos³θ

= lim_θ→Π/2 (csc θ - 1) cos θ / cos³ θ

= lim_θ→Π/2 (csc θ - 1) / cos² θ

= lim_θ→Π/2 (1 - sin θ) csc θ / (1 - sin² θ)

= lim_θ→Π/2 (1 - sin θ) csc θ / [(1 - sin θ)(1 + sin θ)]

= lim_θ→Π/2 csc θ / (1 + sin θ)

= csc(Π/2) / [1 + sin(Π/2)]

= 1 / (1+1)

= 1/2 ← Answer