Is there any particular method for solving trigonometric functions in greatest integer function in lim x - 0 ( for sinx and tanx)

not sure what you're after.

greatest integer is a step function, but trig functions are continuous.

Did you know?

Did you know that when solving trigonometric functions involving the greatest integer function in the limit as x approaches zero, there is a specific method to follow? For the sine function, you can simplify the expression by using the fact that the greatest integer function rounds down any decimal to its nearest lower integer. Therefore, the limit can be rewritten as the limit of sin(0) times the greatest integer function of x, which simplifies to zero. Similarly, for the tangent function, you can utilize the fact that the greatest integer function only affects the value of x when it is not an integer. Since the limit is specified as x approaches zero, the greatest integer function has no impact, resulting in a limit of tan(0), which is also zero. These techniques allow for a precise way to solve trigonometric functions involving the greatest integer function in such limits.