Question

Ajuda, por favor.

Se cosx = 1/3, quanto vale cos2x?

Answer 1

$\boxed{\cos{2x}=\cos^2{x}-\sin^2{x}}\ \therefore\ \boxed{\cos{2x}=2\cos^2{x}-1}$

$\cos{x}=\dfrac{1}{3}\ \therefore\ \cos{2x}=2\bigg(\dfrac{1}{3}\bigg)^2-1\ \therefore$

$\cos{2x}=\dfrac{2}{9}-\dfrac{9}{9}\ \therefore\ \boxed{\cos{2x}=-\dfrac{7}{9}}$