What is taylor 1/((1-0.8*cos^2(x))) ?

The answer to taylor 1/((1-0.8*cos^2(x))) is 5-20x^2+260/3 x^4+\ldots

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taylor 1/((1-0.8*cos^2(x)))

taylor

\frac{1}{( 1 - 0.8 \cdot cos ^{2} ( x ) )}

5 - 20 x^{2} + \frac{260}{3} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 5 + \frac{\frac{d}{d x} ( \frac{1}{1 - 0.8 c o s ^{2} ( x )} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{1 - 0.8 c o s ^{2} ( x )} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{1 - 0.8 c o s ^{2} ( x )} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 5 + \frac{0}{1 !} x + \frac{- 40}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{2080}{4 !} x^{4} + \dots

Refine

= 5 - 20 x^{2} + \frac{260}{3} x^{4} + \dots

\frac{5}{( s ^{2} + 5 )}

\int \frac{4 ln ^{2} ( x ) + 49}{x} d x

f (x) = - x^{2} + 4 x, at x = 4

\frac{d}{d x} (\frac{7 e ^{x} + 4 e ^{- x}}{8})

\frac{d}{d x} (ln (\frac{( x - 4 )}{x - 3}))

What is taylor 1/((1-0.8*cos^2(x))) ?
The answer to taylor 1/((1-0.8*cos^2(x))) is 5-20x^2+260/3 x^4+\ldots