Given that $y={{\sin }^{-1}}x$ , show that $(\cos y)\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}-

Question

Given that $y={{\sin }^{-1}}x$ , show that $(\cos y)\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}-(\sin y){{\left( \frac{\mathrm{d}y}{\mathrm{d}x} \right)}^{2}}=0$. Hence write down the first two non-zero terms in the Maclaurin series for $y$. [5]

Accepted Answer

y=x+x^3/6+...

2013 CJC P1 Q8

2013 CJC P1 Q8

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