Math, asked by mona137, 11 months ago

If y V1--
+* V1-y=1; prove that​

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Answered by hukam0685
0

Step-by-step explanation:

Step-by-step explanation:

We know that

 \frac{d}{dx} \Bigg( \frac{U}{V} \Bigg) =  \frac{V \frac{dU}{dx}  - U \frac{dV}{dx} }{ {V}^{2} }  \\  \\ y =  \frac{ {sin}^{ - 1}x }{ \sqrt{1 -  {x}^{2} } }   \:  \:  \: ...eq1\\  \\  \frac{dy}{dx}  = \frac{ \sqrt{1 -  {x}^{2} }  \frac{d( {sin}^{ - 1}x) }{dx}  - {sin}^{ - 1}x \frac{d( \sqrt{1 -  {x}^{2} } )}{dx} }{ {(  \sqrt{1 -  {x}^{2} ) }}^{2} }  \\  \\  \frac{dy}{dx}   = y_1= \frac{ \sqrt{1 -  {x}^{2} }  \frac{1 }{ \sqrt{1 -  {x}^{2} } }  - {sin}^{ - 1}x \frac{( - 2x )}{2\sqrt{1 -  {x}^{2} } )} }{ {1 -  {x}^{2} }}   \\  \\  \frac{dy}{dx}   = y_1= \frac{ 1   +  x \frac{( {sin}^{ - 1}x )}{\sqrt{1 -  {x}^{2} } } }{ {1 -  {x}^{2} }}   \\  \\   \: from \: eq \: 1 \\  \\  y_1= \frac{ 1   +  x y }{ {1 -  {x}^{2} }}   \\  \\cross \: multiply \\  \\ (1 -  {x}^{2} )y_1 = 1 + xy \\  \\ (1 -  {x}^{2} )y_1-xy = 1\\\\

Hence proved.

Hope it helps you.

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