Addition formulae proof for sin(x + y) and cos(x + y)

[maximus101]

For a fixed y \in R , if
f(x) = [sin(x+y)]-(sin x) (cos y) − (cos x) (sin y)and we let E(x) = [f(x)]^2+[f'(x)]^2.

How do we prove the addition formulae for sin(x + y)and cos(x + y) by applying the Mean Value Theorem to E

 

[LCKurtz]

For a fixed y \in R , if
f(x) = [sin(x+y)]-(sin x) (cos y) − (cos x) (sin y)and we let E(x) = [f(x)]^2+[f'(x)]^2.

How do we prove the addition formulae for sin(x + y)and cos(x + y) by applying the Mean Value Theorem to E

Well, if you were to show E(x) ≡ 0 that would show both f and f' are identically 0.