Question

simplify tanx*secx

Answer 1

\[\tan(x) = {\sin(x) \over \cos (x)}\]\[\sec(x) = {1 \over \cos(x)}\]\[\tan(x) \cdot \sec(x) = {\sin(x) \over \cos(x)} \cdot {1 \over \cos(x)} = {\sin(x) \over \cos^2(x)} = \sin(x) \cdot \sec^2(x)\]
"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.

Answer 2

Would\[\sin(x)\over{1-\sin(x)^{2}}\]
worthy of consideration?

Answer 3

Would\[\sin(x)\over{1-\sin(x)^{2}}\]
be worthy of consideration?

Answer 4

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