Question

sin( π-x) +sin( π+x) =0 unde x poate fi orice numar real
Ajutati-ma va rog!!! Rezolva re completa va rog!!

Answer 1

$sin(\pi - x) + sin(\pi + x) = 0 \: \: \: ,\forall\:x\:\in\:\mathbb{R}$

Metoda I :

Formule :

$sin(\pi - x) = sinx$

$sin(\pi + x) = - sinx$

$sinx - sinx = 0 = > 0 = 0 \: adevarat \: \: \: ,\forall\:x\:\in\:\mathbb{R}$

Metoda II :

Formule :

$sin(a - b) = sinacosb - cosasinb$

$sin(a + b) = sinacosb + cosasinb$

$sin(\pi - x) = sin\pi cosx - cos\pi sinx$

$= sin180° \times cosx - cos180° \times sinx$

$= 0 \times cosx - ( - 1) \times sinx$

$= sinx$

$sin(\pi + x) = sin\pi cosx + cos\pi sinx$

$= sin180° \times cosx + cos180 ° \times sinx$

$= 0 \times cosx + ( - 1) \times sinx$

$= - sinx$

$sinx - sinx = 0 = > 0 = 0 \: adevarat \: \: \: ,\forall\:x\:\in\:\mathbb{R}$

$sin\pi = sin180° = 0$

$cos\pi = cos180° = - 1$