If y = sin-1(sin x), -\(\cfrac{\pi}2\) ≤ x ≤ \(\cfrac{\pi}2\). The

1.	If y = sin-1(sin x), -\(\cfrac{\pi}2\) ≤ x ≤ \(\cfrac{\pi}2\). Then write the value of \(\cfrac{dy}{d\mathrm x}\) for x ∈ (-\(\cfrac{\pi}2\), \(\cfrac{\pi}2\)).
Answer» For x ∈ \((-\cfrac{\pi}2,\cfrac{\pi}2),\) y = sin^-1(sin x) = x So, \(\cfrac{dy}{d\mathrm x}\) = 1

If y = sin-1(sin x), -\(\cfrac{\pi}2\) ≤ x ≤ \(\cfrac{\pi}2\). Then write the value of \(\cfrac{dy}{d\mathrm x}\) for x ∈ (-\(\cfrac{\pi}2\), \(\cfrac{\pi}2\)).

Answer»

For x ∈ \((-\cfrac{\pi}2,\cfrac{\pi}2),\)

y = sin^-1(sin x)

= x

So, \(\cfrac{dy}{d\mathrm x}\) = 1

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