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# Another problem simplifying symbolic trigonometric expressions

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

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## 1 Answer

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You must use trig_reduce():

sage: exp1.trig_reduce()
sin(x1 + x2)


The reverse operation is trig_expand():

sage: exp2 = sin(x1 + x2)
sage: exp2.trig_expand()
cos(x2)*sin(x1) + cos(x1)*sin(x2)

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Asked: 2018-01-11 10:40:29 +0200

Seen: 462 times

Last updated: Jan 11 '18