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Ряд Маклорена для y=cost:
![cost=1-frac{t^2}{2!}+frac{t^4}{4!}-frac{t^6}{6!}+...+frac{(-1)^{n}}{(2n)!}cdot t^{2n}+...=sumlimits _{n=0}^{infty }frac{(-1)^{n}}{(2n)!}cdot t^{2n}; ,\oblast; sxodimosti; ; -infty textless t textless +infty \\\cos^2x=frac{1+cos2x}{2}=frac{1}{2}+frac{1}{2}cdot cos2x\\t=2x; ,; cos2x=1-frac{(2x)^2}{2!}+frac{(2x)^4}{4!}-frac{(2x)^6}{6!}+...+(-1)^{n}cdot frac{(2x)^{2n}}{(2n)!}+...=\\= 1-frac{2^2x^2}{2!}+frac{2^4x^4}{4!}-frac{2^6x^6}{6!}+...+(-1)^{n}cdot frac{2^{2n}x^{2n}}{(2n)!}+... cost=1-frac{t^2}{2!}+frac{t^4}{4!}-frac{t^6}{6!}+...+frac{(-1)^{n}}{(2n)!}cdot t^{2n}+...=sumlimits _{n=0}^{infty }frac{(-1)^{n}}{(2n)!}cdot t^{2n}; ,\oblast; sxodimosti; ; -infty textless t textless +infty \\\cos^2x=frac{1+cos2x}{2}=frac{1}{2}+frac{1}{2}cdot cos2x\\t=2x; ,; cos2x=1-frac{(2x)^2}{2!}+frac{(2x)^4}{4!}-frac{(2x)^6}{6!}+...+(-1)^{n}cdot frac{(2x)^{2n}}{(2n)!}+...=\\= 1-frac{2^2x^2}{2!}+frac{2^4x^4}{4!}-frac{2^6x^6}{6!}+...+(-1)^{n}cdot frac{2^{2n}x^{2n}}{(2n)!}+...](https://tex.z-dn.net/?f=cost%3D1-frac%7Bt%5E2%7D%7B2%21%7D%2Bfrac%7Bt%5E4%7D%7B4%21%7D-frac%7Bt%5E6%7D%7B6%21%7D%2B...%2Bfrac%7B%28-1%29%5E%7Bn%7D%7D%7B%282n%29%21%7Dcdot+t%5E%7B2n%7D%2B...%3Dsumlimits+_%7Bn%3D0%7D%5E%7Binfty+%7Dfrac%7B%28-1%29%5E%7Bn%7D%7D%7B%282n%29%21%7Dcdot+t%5E%7B2n%7D%3B+%2C%5Coblast%3B+sxodimosti%3B+%3B+-infty++textless++t+textless++%2Binfty+%5C%5C%5Ccos%5E2x%3Dfrac%7B1%2Bcos2x%7D%7B2%7D%3Dfrac%7B1%7D%7B2%7D%2Bfrac%7B1%7D%7B2%7Dcdot+cos2x%5C%5Ct%3D2x%3B+%2C%3B+cos2x%3D1-frac%7B%282x%29%5E2%7D%7B2%21%7D%2Bfrac%7B%282x%29%5E4%7D%7B4%21%7D-frac%7B%282x%29%5E6%7D%7B6%21%7D%2B...%2B%28-1%29%5E%7Bn%7Dcdot+frac%7B%282x%29%5E%7B2n%7D%7D%7B%282n%29%21%7D%2B...%3D%5C%5C%3D+1-frac%7B2%5E2x%5E2%7D%7B2%21%7D%2Bfrac%7B2%5E4x%5E4%7D%7B4%21%7D-frac%7B2%5E6x%5E6%7D%7B6%21%7D%2B...%2B%28-1%29%5E%7Bn%7Dcdot+frac%7B2%5E%7B2n%7Dx%5E%7B2n%7D%7D%7B%282n%29%21%7D%2B...)
![cos^2x=frac{1}{2}+frac{1}{2}cdot (1-frac{2^2x^2}{2!}+frac{2^4x^4}{4!}-frac{2^6x^6}{6!}+,,,+(-1)^{n}cdot frac{2^{2n}x^{2n}}{(2n)!}+...)=\\=1-frac{2x^2}{2!}+frac{2^3x^4}{4!}-frac{2^5x^6}{6!}+...+(-1)^{n}cdot frac{2^{2n-1}x^{2n}}{(2n)!}+...\\cos^2x=sumlimits _{n=0}^{infty }frac{(-1)^{n}cdot 2^{2n-1}cdot x^{2n}}{(2n)!}; ,; ; -infty textless x textless +infty cos^2x=frac{1}{2}+frac{1}{2}cdot (1-frac{2^2x^2}{2!}+frac{2^4x^4}{4!}-frac{2^6x^6}{6!}+,,,+(-1)^{n}cdot frac{2^{2n}x^{2n}}{(2n)!}+...)=\\=1-frac{2x^2}{2!}+frac{2^3x^4}{4!}-frac{2^5x^6}{6!}+...+(-1)^{n}cdot frac{2^{2n-1}x^{2n}}{(2n)!}+...\\cos^2x=sumlimits _{n=0}^{infty }frac{(-1)^{n}cdot 2^{2n-1}cdot x^{2n}}{(2n)!}; ,; ; -infty textless x textless +infty](https://tex.z-dn.net/?f=cos%5E2x%3Dfrac%7B1%7D%7B2%7D%2Bfrac%7B1%7D%7B2%7Dcdot+%281-frac%7B2%5E2x%5E2%7D%7B2%21%7D%2Bfrac%7B2%5E4x%5E4%7D%7B4%21%7D-frac%7B2%5E6x%5E6%7D%7B6%21%7D%2B%2C%2C%2C%2B%28-1%29%5E%7Bn%7Dcdot+frac%7B2%5E%7B2n%7Dx%5E%7B2n%7D%7D%7B%282n%29%21%7D%2B...%29%3D%5C%5C%3D1-frac%7B2x%5E2%7D%7B2%21%7D%2Bfrac%7B2%5E3x%5E4%7D%7B4%21%7D-frac%7B2%5E5x%5E6%7D%7B6%21%7D%2B...%2B%28-1%29%5E%7Bn%7Dcdot+frac%7B2%5E%7B2n-1%7Dx%5E%7B2n%7D%7D%7B%282n%29%21%7D%2B...%5C%5Ccos%5E2x%3Dsumlimits+_%7Bn%3D0%7D%5E%7Binfty+%7Dfrac%7B%28-1%29%5E%7Bn%7Dcdot+2%5E%7B2n-1%7Dcdot+x%5E%7B2n%7D%7D%7B%282n%29%21%7D%3B+%2C%3B+%3B+-infty++textless++x+textless++%2Binfty+)
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Спасибо большое решите остальные пожалуйста
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