13. $Ifsi{n}^{-1}x=y,then$

$\begin{array}{l}\left(A\right)0\le y\le \pi \left(B\right)-\frac{\pi }{2}\le y\le \frac{\pi }{2}\\ \left(C\right)0<y<\pi \left(D\right)-\frac{\pi }{2}<y<\frac{\pi }{2}\end{array}$

<p>Given, Sin⁻¹<em>x</em>=y.</p><p> (E) We know that the principal value branch of Sin⁻¹&nbsp;is</p><p><span title="Click to copy mathml"><math><mrow><mrow><mo> [</mo><mrow><mfrac><mrow><mo>−</mo><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>, </mo></mrow></mrow><mrow><mrow><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mo>]</mo></mrow></mrow></math></span>&nbsp;Hence, &nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mo>−</mo><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>&nbsp;≤ y ≤&nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span></p><p>Option B is correct.</p>

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