Question

2. Simplifique a seguinte expressão:
sen (a+b)+ sen (a - b)
cos (a+b)+cos (a - b)​

Answer 1

Resposta:

$\tan{a}$

Explicação passo-a-passo:

$\boxed{\sin{(\theta\pm\phi)}=\sin{\theta}\cos{\phi}\pm\sin{\phi}\cos{\theta}}\\\\ \boxed{\cos{(\theta\pm\phi)}=\cos{\theta}\cos{\phi}\mp\sin{\theta}\sin{\phi}}$

$x=\dfrac{\sin{(a+b)+\sin{(a-b)}}}{\cos{(a+b)}+\cos{(a-b)}}\ \therefore\ \\\\ x=\dfrac{\sin{a}\cos{b}+\sin{b}\cos{a}+\sin{a}\cos{b}-\sin{b}\cos{a}}{\cos{a}\cos{b}-\sin{b}\sin{b}+\cos{a}\cos{b}+\sin{a}\sin{b}}\ \therefore\\\\ x=\dfrac{2\sin{a}\cos{b}}{2\cos{a}\cos{b}}\ \therefore\ \boxed{x=\tan{a}}$