Question

FUNÇOES TRIGONOMÉTRICAS. sejam a e b reais quaisquer verifique que: sen a cos b = 1/2 [sen(a+b) + sen (a-b)]? Ficarei Agradecido!

Answer 1

 Olá Lucas,
boa tarde!

$\frac{\sin(a+b)+\sin(a-b)}{2}=\\\\\frac{(\sin\,a\cdot\cos\,b+\sin\,b\cdot\cos\,a)+(\sin\,a\cdot\cos\,b-\sin\,b\cdot\cos\,a)}{2}=\\\\\frac{\sin\,a\cdot\cos\,b+\sin\,b\cdot\cos\,a+\sin\,a\cdot\cos\,b-\sin\,b\cdot\cos\,a}{2}=\\\\\frac{\sin\,a\cdot\cos\,b+\sin\,a\cdot\cos\,b}{2}=\\\\\frac{2\cdot\sin\,a\cdot\cos\,b}{2}=\\\\\boxed{\sin\,a\cdot\cos\,b}$