What do the limits and have to do with the derivatives of the sine and cosine functions? What are the derivatives of these functions?
Step 1 of 3:
In this problem, we need to explain what do the limits have to do with the derivatives of the sine and cosine functions and we have to find the derivatives of these functions.
Step 2 of 3:
We know that those limits are directly used in calculating the derivatives of sin x and cos x.
So, we firstly solve the derivative of sin x
If we denote we can write
Now we solve
Clearly if we put the limit then we get indeterminate form.
So, we apply L-Hospital Rule
Then, we get
From equation (1)
for any real