[tex]\bf sec(\theta)=\cfrac{1}{cos(\theta)}
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sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\
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sec^2(x)[1-sin^2(x)]=1\\\\
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\textit{checking the left-hand-side}\\\\
\cfrac{1^2}{cos^2(x)}[cos^2(x)]\implies 1[/tex]
