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Symmetrya. Use infinite series to show that cos x is an
Chapter 8, Problem 77AE(choose chapter or problem)
Symmetry
a. Use infinite series to show that cos x is an even function. That is, show cos x = cos (-x).
b. Use infinite series to show that sin x is an odd function. That is, show sin x = -sin (-x).
Questions & Answers
QUESTION:
Symmetry
a. Use infinite series to show that cos x is an even function. That is, show cos x = cos (-x).
b. Use infinite series to show that sin x is an odd function. That is, show sin x = -sin (-x).
ANSWER:Solution 77AE
Step 1:
In this problem we have to prove cos x is an even function and sin x is an odd function using infinite series.
a. Use infinite series to show that cos x is an even function. That is, show
The Taylor series expansion for is
Now to prove that is an even function, we should prove
Put in
Therefore is an even function.