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If X = U V and Y = U V Prove that J J 1 = 1 - Applied Mathematics 1

`"If"  x=uv & y=u/v "prove that"  jj^1=1`

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Solution

`x= uv and y=u/v` 

∴ x and y are function of u and v . 

∴ `u=sqrtxy`      ∴` v= sqrt(x/y)`  ...........{from given eqns} 

`j= |[x_u,x_v],[y_u,y_v] ||[v,u],[1/v, -u/v^2] |=-u/v-u/v=(-2u)/v`   ................(1)

`j^1 =|[u_x,u_y],[v_x,v_y] |=|[sqrty/(2sqrtx),sqrtx/(2sqrty)],[1/(2sqrtxy), -sqrtx/(2ysqrty)] | = -sqrt(x/y)/(2sqrtxy)=-v/2u`

∴` jj^1=(-2u)/vxx(-v)/(2u)=1` 

  ∴` jj^1=1` 

Hence Proved.

Concept: .Circular Functions of Complex Number
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