Sunday 15 March 2015

trigonometry - Solve $left| cos { left( 2x right) } right| = frac { 1 }{ 2 } $

How do you solve the following equation over an unrestricted domain;
$$\left| \cos { \left( 2x \right) } \right| = \frac { 1 }{ 2 } $$



I can solve half of it;




$$\cos { \left( 2x \right) } =\frac { 1 }{ 2 } \\ x=\pi n\pm \frac { \pi }{ 6 } $$



but how do you do the other half
$$\cos { \left( 2x \right) } =-\frac { 1 }{ 2 } $$

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