Question Type 4: Maclaurin product series via coefficient comparison Bootcamps

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

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

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 for $\csc x$ up to the $x^5$ term using $\csc x\,\sin x=1$.

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

Determine the Maclaurin series for $\csc x$ up to the $x^7$ term using $\csc x\,\sin x=1$.

Find the Maclaurin series of $\tan x$ up to the $x^9$ term using $\tan x\cos x=\sin x$.