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I am testing Sage with the notebook interface, and I want to simplify this trigonometric symbolic expression:

var('x1','x2')
exp1=sin(x1)*cos(x2)+sin(x2)*cos(x1)
print(exp1.trig_simplify())

Sage does not simplify this expression and the result is:

cos(x2)*sin(x1) + cos(x1)*sin(x2)

As you can see the result show be:

sin(x1+x2)

Is there any to simplify trigonometric functions applied to the addition or the subtraction of two values? Thanks

I did not know this way for define symbolic functions. Thanks

I am working with the last version recently compiled from the source code.

'SageMath version 8.1, Release Date: 2017-12-07'

I did not want to use mathematical function gamma. I only wanted to define an angle variable. I have just used another name for the symbolic angle variable 'rho' and now it works.

Here it is the code:

var('t,alpha,beta,rho'); 
alpha(t)=function('alpha',t); beta(t)=function('beta',t); rho(t)=function('rho',t);
mi(t)=sin(beta)^2*diff(alpha(t), t) + (cos(beta)*diff(alpha(t), t) +diff(rho(t), t))*cos(beta); 
show(mi(t).expand());
show(mi(t).trig_simplify());

And the expected result:

cos(beta(t))^2*diff(alpha(t), t) + sin(beta(t))^2*diff(alpha(t), t) +
cos(beta(t))*diff(rho(t), t)
cos(beta(t))*diff(rho(t), t) + diff(alpha(t), t)

Thanks Nbruin

Notebook tells it is psi(t). But it is amazing!! It is not defined. And seems to susbtitute 'diff(gamma(t),t)' that it is supposed to be the right answer.

Right answer must be: cos(beta(t))*diff(gamma(t), t) + diff(alpha(t), t)

I am testing Sage with basic simbolic expressions appliying derivatives to some functions f(t). When I try to simplify the trigonometric final expressión Sage Notebook does not recognize the partial derivative symbol. I do not understand the new variable psi(t) that appears in the solution.

Here is the Notebook Sage code:

var('t,alpha,beta,gamma'); 
alpha(t)=function('alpha',t); beta(t)=function('beta',t); gamma(t)=function('gamma',t);
mi(t)=sin(beta)^2*diff(alpha(t), t) + (cos(beta)*diff(alpha(t), t) +diff(gamma(t), t))*cos(beta); 
print(mi(t).expand());
print(mi(t).expand().trig_simplify());

Here is the result:

cos(beta(t))^2*diff(alpha(t), t) + sin(beta(t))^2*diff(alpha(t), t) +
cos(beta(t))*diff(gamma(t), t)
cos(beta(t))*gamma(t)*psi(t) + diff(alpha(t), t)