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

Explanation

To show that \(\frac{dy}{dx} = -\frac{y}{x}\) given that \(x = \sqrt{a^{\sin^{-1} t}}\) and \(y = \sqrt{a^{\cos^{-1} t}}\), we will follow these steps:

### Step 1: Express \(x\) and \(y\) in terms of \(a\)
We have:
\[ x = \sqrt{a^{\sin^{-1} t}} \quad \text{and} \quad y = \sqrt{a^{\cos^{-1} t}} \]

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