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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.

MichaelTheSlav
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2 Answers2

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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
acer
  • 5,293
  • Thank you for answering. Yes, I got confused about tg and tan, partly because by professor himself wrote tg in the assignment, and partly because I always assumed the former to be more common, even though I myself use tan. Also thanks for advice, I will post on Maple Primes next time. – MichaelTheSlav Feb 26 '21 at 22:02
  • I added something for your revised second equation. – acer Feb 27 '21 at 02:15
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For the first equation, this worked:

enter image description here

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

enter image description here

5201314
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  • OK, I was a dumbass, sorry. The second equation is actually arcsin (x) + arccos (x) = Pi/2, not what I wrote. I wrote that correctly in Maple but when i was writing this question I was in the midst of a mental breakdown. Thanks for answering and taking your time. – MichaelTheSlav Feb 26 '21 at 20:59
  • edited my question based on the correct equation – 5201314 Feb 27 '21 at 02:53