What is taylor 1/(1+sin(x)) ?

The answer to taylor 1/(1+sin(x)) is 1-x+x^2-5/6 x^3+2/3 x^4+\ldots

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taylor 1/(1+sin(x))

taylor

\frac{1}{1 + sin ( x )}

1 - x + x^{2} - \frac{5}{6} x^{3} + \frac{2}{3} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 1}{1 !} x + \frac{2}{2 !} x^{2} + \frac{- 5}{3 !} x^{3} + \frac{16}{4 !} x^{4} + \dots

Refine

= 1 - x + x^{2} - \frac{5}{6} x^{3} + \frac{2}{3} x^{4} + \dots

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

\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})

What is taylor 1/(1+sin(x)) ?
The answer to taylor 1/(1+sin(x)) is 1-x+x^2-5/6 x^3+2/3 x^4+\ldots