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Sec s = 1.6948

Cos s = 0.3825

Find the value of s in the interval [0,\(\pi\)/2] that makes the statement true for each.

Please explain process.

Verified Answer :

that'd be true only if the value of "s" is the exact same one for both
namely  if sec(s) = cos(s)
then solving for "s"
thus

\(\bf sec(s)=cos(s)\qquad but\implies sec(\theta)=\cfrac{1}{cos(\theta)} \\\\\\ thus\cfrac{1}{cos(s)}=cos(s)\implies 1=cos^2(s)\implies \pm \sqrt{1}=cos(s) \\\\\\ \pm 1=cos(s)\impliedby \textit{now taking }cos^{-1}\textit{ to both sides} \\\\\\ cos^{-1}(\pm 1)=cos^{-1}[cos(s)]\implies cos^{-1}(\pm 1)=\measuredangle s\)

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