Question

${sin}^{ - 1} x + cos {}^{ - 1} x = \frac{\pi}{2}$
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Answer 1

$\bf \: Let \: \: \: \: {sin}^{ - 1} x = \theta \: \: \: \: \: \: \: \: \: \: \: \: \: .......(1)\\ \\ so \: \: \bf \: \: \: x = \: sin \: \theta \: </p><p></p><p> \\ \\ \bf \: We \: know \: that \: Formula \: \\ \\ \\ \boxed{ \bf \: cos ( \frac{\pi}{2} - \theta )= sin \: \theta} \\ \\ </p><p></p><p>Now, \: putting \: it \: value \\ \\ \\ </p><p></p><p>\bf \: \: cos \: ( \frac{\pi}{2} - \theta) = x \\ \\ \\ \implies \: \bf \: \: ( \frac{\pi}{2} - \theta) = {cos}^{ - 1} x \\ \\ \: lets \: put \: the \: value \: of \: \theta \: from \: the \: first \: equation \\ \\ \\ \implies \: \bf \: \: ( \frac{\pi}{2} - {sin}^{ - 1} x) = {cos}^{ - 1} x \\ \\ \\ \implies \: \boxed{\bf \: \: sin {}^{ - 1}x + cos {}^{ - 1} x = \frac{\pi}{2} }$