Here please, we have new formulas for generating sin(nx) and cos(nx) in functions of integer n and sinx only, or integer n and cosx only.

I am engineer, not expert in mathematics, but sure that they are new  and correct formulas. I've  developped them from known mathematical formulas. Before that, I've put them as empirical formulas and prooved them with means of mathematical induction. Other prooved formulas i did not found, there are some, but not prooved.
One of uses of these formulas, we can see if we try to solve integrals, for example,  sin(nx)  or cos(nx) with  sinx or cosx, such as  cos(2n)x*sinx.
I gently ask experts to give their opinion.

Thanks for them.

Zuhair Omari, Jordan