It is given that $x$ and $y$ satisfy the equation ${{ an }^{-1}}x+{{ an }^{-1}}y+{{ an }^{-1}}\le

Question

It is given that $x$ and $y$ satisfy the equation ${{	an }^{-1}}x+{{	an }^{-1}}y+{{	an }^{-1}}\left( xy ight)=\frac{7}{12}\pi $. Find the value of $y$ when $x=1$. [2] Express $\frac{\mathrm{d}}{\mathrm{d}x}\left( {{	an }^{-1}}\left( xy ight) ight)$ in terms of $x$, $y$ and $\frac{\mathrm{d}y}{\mathrm{d}x}$. [2] Show that, when $x=1$, $\frac{\mathrm{d}y}{\mathrm{d}x}=-\frac{1}{3}-\frac{1}{2\sqrt{3}}$. [2]

Accepted Answer

(i) $\frac{1}{\sqrt{3}}$ (ii) $\frac{1}{1+{{\left( xy ight)}^{2}}}\left( x\frac{\mathrm{d}y}{\mathrm{d}x}+y ight)$ 	ext{ or } $-\frac{1}{1+{{x}^{2}}}-\frac{1}{1+{{y}^{2}}}\left( \frac{\mathrm{d}y}{\mathrm{d}x} ight)$

N2000 P1 Q11

N2000 P1 Q11

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