Question Type 4: Maclaurin product series via coefficient comparison Exercises

Determine the Maclaurin series of $\sec x$ up to and including the $x^6$ term by using $\sec x\,\cos x=1$.

Determine the series expansion for $\csc x$ in powers of $x$ up to and including the term in $x^7$, using the relationship $\csc x \sin x = 1$.

Find the series expansion of $\csc x$ about $x = 0$ up to and including the term in $x^5$, using the relationship $\csc x \sin x = 1$.

Find the Maclaurin series of $f(x)=\sin^2x$ up to and including the $x^6$ term by using the series for $\sin x$ and multiplication.

Compute the Maclaurin series of $f(x)=\sin x\tan x$ up to the $x^7$ term by multiplying their known series.

Find the Maclaurin series expansion of $\tan x$ up to and including the $x^7$ term by using the identity $\tan x\,\cos x=\sin x$.

Find the Maclaurin series of $\tan x$ up to the term in $x^7$ using the relationship $\tan x\cos x=\sin x$.

Obtain the Maclaurin series for $\sec x$ up to the $x^8$ term by using $\sec x\,\cos x=1$.