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## Homework Statement

Using the deﬁnition of continuity, prove that the function f(x) = sin x

is continuous.

Hint: sin a − sin b = 2 sin (a-b)/2 . cos (a+b)/2

## Homework Equations

## 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

Tam

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