Trig simplifying hp50g

[Tugdual]

To me
$$\sin { (x)*\tan { (x) } } $$ is not a simplified version of $$\frac { { \sin { \left( x \right) } }^{ 2 } }{ \cos { \left( x \right) } } $$ it is just another way to write it.

Not sure what the "simplify" functions of 50g and Prime are trying to do but the 50g answer with flag 116 being set to "Prefer cos" $$\frac { 1-{ \cos { \left( x \right) } }^{ 2 } }{ \cos { \left( x \right) } } $$ which presents a certain interest especially since you can now envisage substitution.

Now in order to find a "tan", I would rather use the TRIGT rewriting command that unfortunately returns a pretty silly and ugly result until you press EVAL as mentioned by Thomas earlier. Note that simplifying $$\tan { \left( x \right) *\sin { \left( x \right) } } $$ quite rapidly becomes tedious and mental and you never get any close to the first form. 50g CAS doesn't happen very capable.