1. Limits Involving Trigonometric Functions

2. All trigonometric functions are continuous a each point of their domains, which is R for the sine & cosine functions, R-{ π/2, - π/2, 3π/2, - 3π/2,…………} for the Tangent and the Secant functions and R-{0, π, - π, 3π, - 3π ,…………} for the Cotangent and the Cosecant functions. Thus: The the limit of sinx and cosx at any real number are sina and cosa respectively.

3. Important Identity

4. Examples (1)

9. Example (2)
Solution
f is continuous for all x other than zero. To check, whether it is continues, as well at x=0, we need to that its limit at x=0 is equal to f(0), which is given as zero.