How to find Maclaurin series of $\cos^2(x)$ from $\cos(x)$.

Maclaurin Series of $\cos(x) = 1-\frac{x^2}{2}+.....$

Then how to find for $\cos^2(x)$ from $\cos(x)$.

For the $cos^2(x)$, I thought of just squaring the right hand side.

Please explain me the method.

  • 4
    $\begingroup$ Use $\cos^2(x)=\frac{1+\cos(2x)}{2}$ and then use the MacLaurin Series for cos. $\endgroup$ – aleden Apr 10 '18 at 1:20
  • $\begingroup$ What have you tried? If you know the maclurin series for cos(x) already, what do you have to do to turn cos(x) into cos^2(x)? @josh $\endgroup$ – Tyberius Apr 10 '18 at 1:21

It becomes far easier if you invoke this trig identity. $$\cos^2(x) = {1 + \cos(2x)\over 2}.$$

  • 1
    $\begingroup$ Isn't is, rather, $cos^2(x)$ which is asked ? $\endgroup$ – Duchamp Gérard H. E. Apr 10 '18 at 1:26
  • $\begingroup$ I asked for cos^2(x) $\endgroup$ – user550230 Apr 10 '18 at 1:28

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