76. Discuss the continuity of the cosine, cosecant, secant and cotangent functions.

(i) Let f(x) = cos x. D_f = R
Let a be any real number ∈ D_f

∴ f is continuous as x = a
But a is any real number ∈ D_f
∴ f is continuous at every point of its domain.
i.e., cos x is continuous at every point of its domain.

∴ f is continuous at x = a
But a is any real number ∈ D_f
∴ f is continuous function at every point of domain,
∴ cosec x is continuous at every point of domain.

∴ f is continuous at x = a
But a is any real number ∈ D_f
∴ f is continuous at every point of domain,
∴ sec x is continuous at every point of domain.

∴ f is continuous at x = a.
But a is any real number ∈ D_f.
∴ f is continuous at every point of domain,
∴ cot x is continuous at every point of domain.