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

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

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To solve the problem, we need to show that \(\frac{dy}{dx} = -\frac{y}{x}\) given the equations \(x = \sqrt{a^{\sin^{-1} t}}\) and \(y = \sqrt{a^{\cos^{-1} t}}\). ### Step 1: Differentiate \(x\) with respect to \(t\) Given: \[ x = \sqrt{a^{\sin^{-1} t}} = a^{\frac{1}{2} \sin^{-1} t} \] ...
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