With HP50G,approx mode (but exact mode is OK):
Code:
'SIN(X)=COS(X)' SOLVEVX
{ X 'LN(X)'} Lsub
{ n1 n n2 n } Lsub
SOLVEVX
here,you get :
Code:
{ 'X=EXP(6.2832*n-2.3562)'
'X=EXP(6.2832*n+0.7854)' }
Then you can test with some n values
Note that Lsub is a program I use for | (or SUBST) when equations are in a list (list processing don't work with | or subst) :
Code:
« 1 ->LIST { | } + ->PRG MAP »
I also often use Lexr to get only the right part of equations in a list :
Code:
« 1 « EXLR NIP » DOSUBS »
Ex :
{ 'X=EXP(6.2832*n-2.3562)'
'X=EXP(6.2832*n+0.7854)' }
Lexr
gives
{ 'EXP(6.2832*n-2.3562)' 'EXP(6.2832*n+0.7854)' }
and for example to test n from -5 to 5, continue with
STEQ {}
-5 5 FOR a
EQ 'n' a 2 ->LIST Lsub +
NEXT
XNUM SORT
that gives
{ 2.1526E-15 4.9812E-14 1.1527E-12 2.6674E-11 6.1725E-10 1.4284E-8 3.3053E-7 7.6487E-6 0.0002
0.0041 0.0948 2.1933 50.7540 1174.4832 27178.3539 628925.9347 14553781.7413 336784589.923 7793428678.94 180345337617. 4.1733E12 9.6573E13 }
In exact mode you get
{ 'EXP(2*ATAN(-1+√2)-2*PI)' '1/EXP(2*ATAN(1+√2))' 'EXP(2*ATAN(-1+√2))' }
As you see the HP don't simplify the ATAN (but you can write easily your own program for trivial trig simplifications with a serie of MATCH commands. But it's not automatic and rather slow). I can post this if there is some intesrest
with the Prime
solve(sin(ln(x))=cos(ln(x)))
returns directly the symbolic simplified general solution... ( 'principal' uncheck in CAS setting)
It would fine if we could do :
equation | n={-1,0,1,2}
or
equation | n={-5...5}
to obtain a list of equations for each value.
But this dont work ....
So I do this:
Edit the general solution to change n_xxx by n
then
f(n):=ANS
concat(f(-1),f(0))
concat(ANS,f(1))
concat(ANS,f(2))
sort(ans)
~=
and you get the result (approx or exact)