Why is this trigonometric expression with $\arctan$ not simplified ?

ArcTan[Tan[γ[t] - θ[t]]]

1 Answer 1



Plot[{ArcTan[Tan[a]], a}, {a, -Pi, Pi},
 PlotLegends -> "Expressions"]

enter image description here

Consequently, some assumptions are needed to get the simplification

Assuming[{-Pi/2 < γ[t] - θ[t] < Pi/2}, 
 Simplify[ArcTan[Tan[γ[t] - θ[t]]]]]

(*  γ[t] - θ[t]  *)

Or use PowerExpand

ArcTan[Tan[γ[t] - θ[t]]] // PowerExpand

(*  γ[t] - θ[t]  *)

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.