Analysis problem using the Lagrange Remainder Theorem

[shan1732]

Homework Statement

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

The Attempt at a Solution

Let f(x)= $\left|sin\left(x+h\right)-\left(sinx-hcosx\right)\right|$?
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 $\frac{h^{2}}{2}$

 

[micromass]

Hi shan1732!

Try to calculate the Taylor polynomial of the sine around x.