find the principal value of
[tex] { \sin( \frac{1}{ \sqrt{2} } ) }^{ – 1} [/tex]
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1 thought on “find the principal value of<br />[tex] { \sin( \frac{1}{ \sqrt{2} } ) }^{ – 1} [/tex]<br />​”

1. [tex]\huge\underline\bold\red{★Answer★}[/tex]

   [tex]let \: \: \: y = {sin}^{ – 1} ( \frac{1}{ \sqrt{2} } ) \\ siny = \frac{1}{ \sqrt{2} } \\ y = \frac{\pi}{4} \\ since \: \: range \: \: of \: \: {sin}^{ – 1} \: is \: – \frac{\pi}{2} \leqslant x \leqslant \frac{\pi}{2} \\ \therefore \: \: principal \: \: value \: \: of \: \: {sin}^{ – 1} ( \frac{1}{ \sqrt{2} } ) \: \: is \: \: \frac{\pi}{4} [/tex]

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