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If $u=\sin^{-1}\begin{pmatrix}\large\frac{x^{4}+y^{4}}{x^{2}+y^{2}}\end{pmatrix}$ and $f=\sin u$ then $f$ is a homogeneous function of degree

\[\begin{array}{1 1}(1)0&(2)1\\(3)2&(4)4\end{array}\]

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$\sin u =\begin{pmatrix}\large\frac{x^{4}+y^{4}}{x^{2}+y^{2}}\end{pmatrix}$
Replace x by tx ad y by ty
$\sin u =\large\frac{(tx)^4 +(ty)^4}{(tx)^2+(ty)^2}$
$\qquad= \large\frac{t^4 x^4 +t^4y^4}{t^2x^2 +t^2 y^2}$
$\qquad= \large\frac{t^4 (x^4+y^4)}{t^2(x^2+y^2)}$
$\qquad= t^2 \large\frac{(x^4+y^4}{(x^2+y^2)}$
$f= \sin u$ is a homogeneous function of degree 2.
Hence 3 is the correct answer.
answered May 20, 2014 by meena.p
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