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Find the principal value of sin–1 (\(\frac{1}{\sqrt2}\)) |
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Answer» Let sin–1 (\(\frac{1}{\sqrt2}\)) = x ∴ sin x = \(\frac{1}{\sqrt2}\) ∴ sin x = -sin \(\frac{π}{4}\) The principal value branch of sin–1 x is [\(-\frac{π}{2},\) \(\frac{π}{2}\)] and \(-\frac{π}{2}\) ≤ \(-\frac{π}{4}\) ≤ \(\frac{π}{2}\) Hence, the required principal value of x is\(-\frac{π}{4}\) |
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