Question

cosx=cos(pi/3-x)dentre os valores de x,qual valor satisfaz?

Answer 1

Resolução:

$\cos(x) = \cos( \frac{\pi}{3} - x ) \\ \cos(x) = \cos( \frac{\pi}{3} ) \cos(x) + \sin( \frac{\pi}{3} ) \sin(x) \\ \cos(x) (1 - \frac{1}{2} ) = \frac{ \sqrt{3} }{2} \sin(x) \\ \frac{1}{2} \cos(x) = \frac{ \sqrt{3} }{2} \sin(x) \\ \frac{ \sin(x) }{ \cos(x) } = \frac{ \sqrt{3} }{3} = \tan(x) \\ x = \frac{\pi}{6}$