## anonymous 5 years ago simplify tanx*secx

1. anonymous

$\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.

2. anonymous

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

3. anonymous

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

4. anonymous

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