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If x = sqrt(a^(sin^(-1)t)) , y = sqrt(a...

If `x = sqrt(a^(sin^(-1)t)) , y = sqrt(a^(cos^(-1)t)` then show that,`dy/dx=-y/x.`

Text Solution

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`x=sqrt(a^(sin^(-1)t)),y=sqrt(a^(cos^(-1)t))`
`"or "xcdoty=sqrt(a^(sin^(-1)t+cos^(-1)t))=sqrt(a^(pi//2))`
Differentiating w.r.t. x, we get
`x(dy)/(dx)+y=0`
`"or "(dy)/(dx)=(-y)/(x)`
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