Question

( 2 cos x – sec x). cos x = cos 2x

Answer 1

¡Hola!

$(2 \cos(x) - \sec(x) ) ^. \cos(x) = \cos^{2} (x) \\ \\ \cos(x) .2 \cos(x) - \cos(x). \frac{ 1}{ \cos(x) } = \cos^{2} (x) \\ \\ 2 \cos^{2} (x) - 1 = \cos^{2} (x) \\ \\ 2 \cos ^{2} (x) - \cos^{2} (x) = 1 \\ \\ \ \sqrt{cos ^{2} (x) } = \sqrt{1} \\ \\ \cos(x) = 1 \\ \\ x = \cos ^{ - 1}(1) \\ \\ \boxed{x _{1} = 0 ^{ \circ}} \\ \\ x = 0 + 360 \\ \\ \boxed{x_{2} = 360 ^{ \circ}}$

Los ángulos de x son:

$x = \big\{x _{1} = 0 ^{ \circ} \: x_{2} = 360 ^{ \circ} \big\}$

Espero que sirva y saludos.