# Mathematica is not simplifying trignometric functions under Abs although I provide assumptions

I am trying to simplify a simple expression,

(1/2)*((-Pi)*Abs[Sin[t]] -
Pi*Abs[Sin[t - 2*Pi]] -
2*Pi*Abs[Sin[t - Pi]] + 4)


i.e $$\frac{1}{2} (-2 \pi \left| \sin (t-\pi )\right| -\pi \left| \sin (t-2 \pi )\right| -\pi \left| \sin t\right| +4)$$ for $$0, which should be $$\frac{1}{2} (1 -4\pi |\sin(t)|)$$. I have tried various methods, like ComplexExpand and then FullSimplify[] which gives me,

  (1/2)*Pi*Sqrt[Sin[t - 2*Pi]^
2] - Pi*Sqrt[Sin[t - Pi]^
2] + 2


i.e $$-\pi \sqrt{((t-\pi ) \sin )^2}-\frac{1}{2} \pi \sqrt{((t-2 \pi ) \sin )^2}-\frac{1}{2} \pi \sqrt{(t \sin )^2}+2$$ which I understand shouldn't further simplify as square-root brings in an ambiguity, somehow ComplexExpand is making the expression complicated.

• "I have tried various methods, like ComplexExpand and then FullSimplify[]" Then please show exactly what you did. – Henrik Schumacher Apr 11 '19 at 14:14
• Assuming[0 < t < Pi, (1/2)*((-Pi)*Abs[Sin[t]] - Pi*Abs[Sin[t - 2*Pi]] - 2*Pi*Abs[Sin[t - Pi]] + 4) // Simplify] evaluates to 2 - 2 Pi Sin[t] – Bob Hanlon Apr 11 '19 at 15:02

What's wrong with

Simplify[
(1/2)*((-Pi)*Abs[Sin[t]] - Pi*Abs[Sin[t - 2*Pi]] - 2*Pi*Abs[Sin[t - Pi]] + 4)
]


2 - 2 π Abs[Sin[t]]

?

At least, that's what version 11.3 returns to me.

• Ok let me download the latest Mathematica and try. – Jaswin Apr 11 '19 at 15:14