How do I compare two expressions in Maple to see if they’re equivalent?

Question

I have to compare two expressions as an assignment but the professor didn’t explain how to do it (I doubt he actually knows how to do the stuff he asks us to do). The two expression pairs in question:

tg(x) + tg(y) = (sin(x+y))/cos(x)*cos(y)

arcsin(x) + arcsin(y) = pi/2

Now I know these are true, but whenever I use evalb or is I invariably get false. I tried many different things but none of them work and I’ve searched the internet for help but I didn’t find anything useful. The most similar thing to mine was this but I tried the solution and it didn’t work. Please help, I’m losing my sanity.

Answer 1

For the first equation, this worked:

For the second equation, it appears that the same method didn't simplify it to 0 automatically. Converting arcsin() to arccos() solved the problem:

Answer 2

You may have mistyped tg(...) when you actually mean tan(...), where tan is the name of a trigonometric function in Maple.

In that case you seem to be missing brackets in the right hand side of the first equation. Note the difference in the output that the extra pair of brackets makes:

tan(x) + tan(y) = (sin(x+y))/cos(x)*cos(y);

                     sin(x + y) cos(y)
   tan(x) + tan(y) = -----------------
                          cos(x)


tan(x) + tan(y) = (sin(x+y))/(cos(x)*cos(y));

                      sin(x + y)
   tan(x) + tan(y) = -------------
                     cos(x) cos(y)

And now,

eq1 := tan(x) + tan(y) = (sin(x+y))/(cos(x)*cos(y)):

is(eq1);

             true

For your second equation, note that the well-known constant is spelled Pi in Maple. The lowercase name pi has no special meaning to Maple.

You might try the solve command, as one way to reformulate the implied relationship between x and y. Eg,

 eq2 := arcsin(x) + arcsin(y) = Pi/2:

 solve(eq2);

                    2     1/2
     {x = x, y = (-x  + 1)   }

This forum is for mathematics, and questions about Maple syntax and programming are better suited to stackoverflow.com or www.mapleprimes.com (the Maplesoft user community).

[edit] You provided a revision to your second equation in a comment to another answer.You gave it as,

eq2 := arcsin(x) + arccos(x) = Pi/2:

Note the conversion,

convert(arcsin(x), arccos);

     1/2*Pi - arccos(x)

And so these all work here.

convert((lhs-rhs)(eq2),ln);

           0

convert((lhs-rhs)(eq2),arcsin);

           0

convert((lhs-rhs)(eq2),arccos);

           0