CODEWITHSUNDEEP
pythonsympy
Dimitris
Dimitris

Reputation: 579

Error in SymPy's simplify with trigometric identity

I apologize if I am missing something fundamental. I am new in SymPy. The problem arises with the trigonometric identity

$$\sin^3x\cos^3 x = \frac{3\sin 2 x-\sin 6x}{32}$$

With Mathematica's Simplify

Simplify[Sin[x]^3 Cos[x]^3 == (3 Sin[2 x] - Sin[6 x])/32]  (*returns True*)

With SymPy

import sympy as sy
sy.simplify(sy.sin(x)**3*sy.cos(x)**3 == (3*sy.sin(2*x) - sy.sin(6*x))/32)  # returns False

Upvotes: 0

Views: 83

Answers (2)

Dimitris
Dimitris

Reputation: 579

I found that the following approach also works:

sy.simplify(sy.expand(exp2,trig=True))==exp1  #returns True

Thanks to @ForceBru for pointing me out that the == operator compares two expressions for exact structural equality, not algebraic equivalence. I learn that one should simplify or expand expressions before comparing them with ==.

Upvotes: 0

ForceBru
ForceBru

Reputation: 44838

Try using sympy.Eq instead of ==:

sy.Eq(sy.sin(x)**3*sy.cos(x)**3, (3*sy.sin(2*x) - sy.sin(6*x))/32)

== will compare the two symbolic representations for equality on-the-spot, while sympy.Eq represents an equation.

In [19]: sy.simplify(sy.Eq(sy.sin(x)**3*sy.cos(x)**3, (3*sy.sin(2*x) - sy.sin(6*x))/
    ...: 32))                                                                       
Out[19]: True

Upvotes: 3

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