simplify tanx*secx

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simplify tanx*secx

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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\[\tan(x) = {\sin(x) \over \cos (x)}\]\[\sec(x) = {1 \over \cos(x)}\]\[\tan(x) \cdot \sec(x) = {\sin(x) \over \cos(x)} \cdot {1 \over \cos(x)} = {\sin(x) \over \cos^2(x)} = \sin(x) \cdot \sec^2(x)\] "simplify" is somewhat ambiguous; in some contexts it means "express in terms of sin and cos", in others "express with no denominators", and so on.
Would\[\sin(x)\over{1-\sin(x)^{2}}\] worthy of consideration?
Would\[\sin(x)\over{1-\sin(x)^{2}}\] be worthy of consideration?

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Other answers:

It's usually simpler to have all terms be trig functions, not constants. You could just as easily use \[\sin(x) \cdot \left ( 1 + \tan^2(x) \right )\]

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