Question

dado senx=1/3, determine cos2x

Answer 1

Utilizando a identidade

$\cos 2x=1-2\mathrm{\,sen^{2}\,}x$


temos

$\cos 2x=1-2\cdot \left(\dfrac{1}{3} \right )^{2}\\ \\ \cos 2x=1-2\cdot \dfrac{1}{9}\\ \\ \cos 2x=1-\dfrac{2}{9}\\ \\ \cos 2x=\dfrac{9-2}{9}\\ \\ \boxed{\cos 2x=\dfrac{7}{9}}$