how to simplify half angle trigonometric function

[chaowen guo]

Hi:

My formula has a lot of square of half angle trigonometric functions. We all know that sin(x/2)**2=(1-cos(x))/2 and cos(x/2)**2=(1+cos(x))/2. But how to do that in sympy? I try trigsimp and expand_trig, both of them are not working.

import sympy
x=sympy.symbols('x',real=True)
sympy.expand_trig(sympy.cos(x/2)**2)
sympy.trigsimp(sympy.sin(x/2)**2)

output is the original half angle formula.

Is there any function like trigreduce in maxima? It does such job.

[Shekhar Prasad Rajak]

HI,

Also feel similar kind of problem. In your case you can do 

>>> from sympy.simplify.fu import fu

>>> fu(S.Half - cos(2*x)/2)

# o/p:    sin(x)**2

>>> from sympy.simplify.fu import TR7

>>> TR7(cos(x)**2)

# o/p:    cos(2*x)/2 + 1/2

Hope these will help.

--

Shekhar

[Shekhar Prasad Rajak]

You can also try this 

In [ ]: from sympy.simplify.trigsimp import trigsimp_groebner

In [ ]: trigsimp_groebner(sin(x/2)**2, hints=[2])

Out[ ]: 

  cos(x)   1

- ────── + ─

    2      2

In [ ]: trigsimp_groebner(cos(x/2)**2, hints=[2])

Out[ ]: 

cos(x)   1

────── + ─

  2      2

--

Shekhar

http://s-hacker.info/

On Tuesday, 31 May 2016 03:43:06 UTC+5:30, chaowen guo wrote: