2021 HCI P1 Q9
Given that $y={{\left( \tan x+\sec x \right)}^{2}}$, show that $\cos x\frac{\text{d}y}{\text{d}x}=2y$.
[2]
(i)
By repeat differentiation, find the Maclaurin series for y up to and including the term in ${{x}^{3}}$.
[4]
(ii)
Using the result obtained in (i) estimate the value of $\tan 1{}^\circ +\sec 1{}^\circ $ to $4$ decimal places.
[2]
(iii)
By expressing $y$ in terms of sine and cosine, use the standard series in MF26 to find the series expansion for $y$ up to and including the term in ${{x}^{3}}$.
[3]
(iv)
Comment on the results obtained from part (i) and part (iii).
[1]
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