Using the deﬁnition of continuity, prove that the function f(x) = sin x
Hint: sin a − sin b = 2 sin (a-b)/2 . cos (a+b)/2
The Attempt at a Solution
Using the idea that:
|sin(x)| ≤ |x|
|cos(x)| ≤ 1
along with the hint: sin a − sin b = 2 sin (a-b)/2 . cos (a+b)/2
We can write:
|sin(a) - sin(b)| ≤ |a - b|
I'm assume we could maybe use this to show how f(x) = sin x is continuous..
What do you think?
Regards as always