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## Homework Statement

Prove that for every pair of numbers x and h, [itex]\left|sin\left(x+h\right)-\left(sinx+hcosx\right)\right|\leq\frac{h^{2}}{2}[/itex]

## The Attempt at a Solution

Let f(x)= [itex]\left|sin\left(x+h\right)-\left(sinx-hcosx\right)\right|[/itex]?

and then to center the taylor polynomial around 0 let h=0? I'm not sure how to get the taylor polynomial for this so that it can be compared to [itex]\frac{h^{2}}{2}[/itex]