sin x , cos x

[alex2008]

Aratati ca :

\( a\cdot \sin x+b\cdot \sin2x=a\cdot \cos x+b\cdot \cos2x , (\forall) x\in \mathbb{R} \Longleftrightarrow a=b=0 \) .

[red_dog]

"\( \Rightarrow \)"

\( x=\frac{\pi}{2}\Rightarrow a=-b \) (1)

\( x=\pi\Rightarrow 0=-a+b\Rightarrow a=b \) (2)

Din (1) si (2) rezulta \( a=b=0 \)

"\( \Leftarrow \)": evident