SOLUTION: let f(x) = cos x. Prove that... [f(x+h) - f(x)]/h = cosx[(cosh-1)/h]- sinx[sinh/h] I have no clue how to do this one.

Question 188287: let f(x) = cos x. Prove that...
[f(x+h) - f(x)]/h = cosx[(cosh-1)/h]- sinx[sinh/h]
I have no clue how to do this one.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: this is one of the many trig identities

Since , this means that or simply

Start with the given expression

Plug in and

Remove the parenthesis and rearrange the terms (I just moved the last cosine term right after the first term)

Factor the term from the first two terms.

Break up the fraction

So where

Note: if you are in Calculus, then this would show that the derivative of is (with a few more steps).
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