What is maclaurin cos^2(x) ?

The answer to maclaurin cos^2(x) is 1-x^2+1/3 x^4-2/45 x^6+1/315 x^8+\ldots

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maclaurin cos^2(x)

maclaurin

cos^{2} (x)

1 - x^{2} + \frac{1}{3} x^{4} - \frac{2}{45} x^{6} + \frac{1}{315} x^{8} + \dots

Solution steps

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( cos ^{2} ( x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( cos ^{2} ( x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( cos ^{2} ( x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{8}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 32}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{128}{8 !} x^{8} + \dots

Refine

= 1 - x^{2} + \frac{1}{3} x^{4} - \frac{2}{45} x^{6} + \frac{1}{315} x^{8} + \dots

(x^{2} - y^{2}) (\frac{d y}{d x}) = 2 x y

\frac{d}{d x} (\frac{sin ( x )}{1 + x ^{2}})

\int sin (π t) cos (π t) d t

\frac{d}{d x} (16 e^{4 x})

\frac{d}{d x} (\frac{x}{3} - \frac{3}{x})

What is maclaurin cos^2(x) ?
The answer to maclaurin cos^2(x) is 1-x^2+1/3 x^4-2/45 x^6+1/315 x^8+\ldots