Updates:
Status: Fixed
Comment #9 on issue 1181 by [email protected]: Advanced trigonometric
simplification
http://code.google.com/p/sympy/issues/detail?id=1181
The OP expresions now give
eq3=r**2*cos(theta)**2*sin(phi)**2
eq1=cos(theta)**2 + cos(phi)**2*sin(theta)**2 +
sin(phi)**2*sin(theta)**2
eq2=r**2*sin(theta)**2 + r**2*cos(phi)**2*cos(theta)**2 +
r**2*cos(theta)**2*sin(phi)**2
eq3=r**2*cos(phi)**2*sin(theta)**2 + r**2*sin(phi)**2*sin(theta)**2
[trigsimp(eq) for eq in (eq1, eq2, eq3)]
[1, r**2, r**2*sin(theta)**2]
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