How does sin* 1/cos give tan sec

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How does sin* 1/cos give tan sec

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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I know 1/cos is sec but where does tan come from?
never mind its cos^2
\[\tan = \frac{ 1 }{ \color{reD}{\cot} }\] cot = cos /sin so \[\tan = \frac{ 1 }{ \color{reD}{\frac{ \cos }{ \sin }} }\] multiply 1 with the reciprocal of the bottom fraction \[\tan =\frac{ \sin }{ \cos }\] lolol

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ohh okay I was like what type of question is this :P lol

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