$1/3$ $1fa=sin^{-1}\left(\dfrac {x^{1/3}+y} {x^{1\sqrt{2} }+y^{1/2}}\right)^{1/2}$ $,$ prove that $x^{2}\dfrac {a^{2}n} {x^{2}}+2xy\dfrac {θ^{2}n} {bx0y}+y^{2}\dfrac {θ^{2}n} {y^{2}}=\dfrac {tann} {144}\left(13+tan^{2}n\right)$

$1$ $1ix=sin^{-1}\left(\dfrac {x} {y}\right)+tan^{-1}\left(\dfrac {y} {x}\right)$ then prove that $x\dfrac {G} {a}+y-$ $5$ $=0.$ $m\right)$ $1f_{x}=f\dfrac {y} {x}\right)$ then prove that $x\dfrac {δz} {δx}+y\dfrac {δz} {δ}$ $=0.$ () $1tx=xyf\left(\dfrac {x} {y}\right)$ prove that $x\dfrac {δz} {ax}+y\dfrac {δz} {0}=2z$ (vi) If $z=xytan\dfrac {y} {x},$ prove that $x\dfrac {0z} {ax}+y\dfrac {0z} {0}=2z$ $-\dfrac {1} {2}$ $\left(m\right)$ $\left(x=\left(1-2xy+y^{2}\right)$ $1$ , prove that $δ2$ $x--y\dfrac {δz} {0}=y^{2}z^{3}$

$8$ $\left(1$ Point) $1\right)$ The\ reciprocal\\ $0+11\right)$ \left(\frac{2} $c\left(2\right)$ {5}\right)^0\ $\right)$ \ $1111s\right)$ $S$ $S1S$ $s3S$ $S4S$ $s2S$