I want to know why [5-5cos(square)(filter)] is equal to [5sin(square)(filter)]

Do you guys know what I mean? sorry for that I can't type (square and filter) signs

First of all, what is this "filter" you are talking about?

Is "filter"supposed to be a variable.
I will assume that it is, and will replace it with x
so you state
5 - 5cos √x = 5sin √x
Secondly, this is not true for all x's as you state.
All I need in one counterexample to show the equation is not true as an identity.
e.g. let x = .25
LS = 5 - 5cos √.25
= 5 - 5cos .5
= .621...
RS = 5sin √.25
= 5sin .5 = 2.39...

Are you solving the equation?
Let me know before I get into that.