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I would like to silmplify a trigonometric equation with some power 2. I'm sure this equation can be reduced but i didn't manage tyo simplify it with Mathematica.

May you help me to simplify this trigonometric equation?

Expr=(1/(cr^4))(4 cr^2 (zP3 - zP4 + pr (Cos[γ3] - Cos[γ4]) + 
     mr (Cos[γ3 - ϕ3] - Cos[γ4 - ϕ4]))^2 + 
  4 cr^2 (-xP3 + xP4 + pr (-Sin[γ3] + Sin[γ4]) + 
     mr (-Sin[γ3 - ϕ3] + 
        Sin[γ4 - ϕ4]))^2 - ((xP3 - xP4)^2 + (zP3 - 
      zP4)^2 - 2 pr^2 (-1 + Cos[γ3 - γ4]) - 
    2 mr^2 (-1 + Cos[γ3 - γ4 - ϕ3 + ϕ4]) + 
    2 pr ((zP3 - zP4) (Cos[γ3] - Cos[γ4]) + (xP3 - 
          xP4) (Sin[γ3] - Sin[γ4])) - 
    2 mr (-(zP3 - zP4) (Cos[γ3 - ϕ3] - 
          Cos[γ4 - ϕ4]) + 
       pr (Cos[γ3 - γ4 - ϕ3] - Cos[ϕ3] - 
          Cos[ϕ4] + 
          Cos[γ3 - γ4 + ϕ4]) + (xP3 - 
          xP4) (-Sin[γ3 - ϕ3] + 
          Sin[γ4 - ϕ4])))^2)

I would like simplification if time the pattern cos()^2+sin()^2 appears.

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  • $\begingroup$ Are you after Simplify@TrigExpand@Expr? $\endgroup$ – corey979 Sep 20 '16 at 15:19
  • $\begingroup$ Do you have some ideas to reduce this expression ? The FullSimplify function doesn't permit to reduce the power 2. Thank you for your help $\endgroup$ – Bendesarts Sep 21 '16 at 8:28

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