Thank you!
On Friday, February 27, 2015 at 5:41:07 PM UTC+2, vdelecroix wrote:
>
> Here is one way... not sure it is the best
>
> sage: eq1 = sqrt(cos(4*x)+1)
> sage: eq2 = eq1.simplify_trig()
> sage: eq2
> sqrt(8*cos(x)^4 - 8*cos(x)^2 + 2)
>
> The next step consists in factoring what is inside the sqrt:
>
> sage: o = eq2.operands()[0]
> sage: of = o.factor()
> sage: o
> 8*cos(x)^4 - 8*cos(x)^2 + 2
> sage: of
> 2*(2*cos(x)^2 - 1)^2
> sage: eq3 = eq2.subs({o:of})
> sage: eq3
> sqrt(2)*sqrt((2*cos(x)^2 - 1)^2)
>
> Then for the conversion sqrt(x^2) -> abs(x) you can use
>
> sage: eq3.simplify_real()
> sqrt(2)*abs(2*cos(x)^2 - 1)
>
> Vincent
>
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