Simplifying trigonometric expression

[Paul Royik]

I'm trying to simplify a*cos(b)**2+a*sin(b)**2 to a

So, I write

a = sympy.Wild('a')

b = sympy.Wild('b')

expr = 49*cos(x)**2+49*sin(x)**2 + 5

expr.replace(a*sympy.sin(b)**2+a*sympy.cos(b)**2, a, exact=True)

But this doesn't work. expr is unchanged.

[Oscar Benjamin]

How about:

>>> x = Symbol('x')
>>> trigsimp(49*cos(x)**2 + 49*sin(x)**2 + 5)
54

Or is your question about the fact that expr.replace does not modify
expr but rather returns a different expression? Maybe you wanted
something like:

expr = expr.replace(...)

--
Oscar

[Shekhar Prasad Rajak]

You can use this :

a,b,c = symbols('a b c')

expr = 49*cos(x)**2+49*sin(x)**2 + 5

expr.replace(a*sin(b)**2+a*cos(b)**2, a, exact=True)

# output 49*sin(x)**2 + 49*cos(x)**2 + 5

[Aaron Meurer]

I think replace doesn't match subexpressions in an Add, because it
isn't a subtree in the expression tree. This sort of thing needs to be
improved.

This workaround seems to work

In [23]: c = Wild('c', exclude=[sin(x), cos(x)])

In [24]: expr.replace(a*sympy.sin(b)**2+a*sympy.cos(b)**2 + c, a + c)
Out[24]: 54

However, putting the right thing in the exclude parameter is
important. Otherwise, you get stuff like

In [16]: c = Wild('c')

In [17]: expr.replace(a*sympy.sin(b)**2+a*sympy.cos(b)**2 + c, a + c)
Out[17]:
2 2
- 49⋅sin (x) - 49⋅cos (x) + 103

which is technically correct (49 + 5 = -49 + 103), but probably not
what you want.

Aaron Meurer

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