get sympy result as trig function rather than complex log

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I'm doing some manipulation of trig equations and would like the results back in trig form.

What I'm doing is this:

from sympy import *
B,D,a=symbols(r'B,D,alpha',real=True,positive=True)
eq1=Eq(D,B*((sin(a)*sin(a))/(sin(a+a))))
solve(eq1,a)

I expect the result to be atan(2*D/B) but I'm getting:

[-I*log(-sqrt((B + 2*I*D)/(B - 2*I*D))), -I*log((B + 2*I*D)/(B - 2*I*D))/2]

I know sympy is expanding the trig functions into exponential form, but I can't seem to convince it to convert the results back.

I've tried:

[n.rewrite(atan) for n in solve(eq1,a)]

but I get the same result back...

sympy trigonometry python
1 Answers

If you simplify before solving, the result looks better. 

>>> solve(eq1.simplify(), a)
[atan(2*D/B)]

Also, the more mathematically rigorous solveset (a modern alternative to solve) returns a more mathematically correct answer without the need for simplification:

>>> solveset(eq1, a)
ConditionSet(alpha, Eq(tan(alpha)/2 - D/B, 0), Reals)

The point being that there are infinitely many solutions, so they cannot be given as a list: so, solveset presents them as the set of all alpha such that tan(alpha) is 2*D/B.

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