### 2018 MJC Promo Q8

2018 MJC Promo Q8 (a) (i) Given that $y=cos left( {{text{e}}^{2x}}-1 right)$, show that $frac{{{text{d}}^{2}}y}{text{d}{{x}^{2}}}-2frac{text{d}y}{text{d}x}+4y{{text{e}}^{4x}}=0$. By further differentiation of this result, find the Maclaurin series of the function $cos left(