Question

1/2+cos^2•3x/2-sin^2•3x/2=0

Answer 1

$\frac{1}{2} + { \cos( \frac{3x}{2} ) }^{2} - { \sin( \frac{3x}{2} ) }^{2} = 0 \\ \ { \sin(x) }^{2} = 1 - { \cos(x) }^{2} \\ \frac{1}{2} + { \cos( \frac{3x}{2} ) }^{2} - 1 + { \cos( \frac{3x}{2} ) }^{2} = 0 \\ 2{ \cos( \frac{3x}{2} ) }^{2} = \frac{1}{2} \\ { \cos( \frac{3x}{2} ) }^{2} = \frac{1}{4} \\ \cos( \frac{3x}{2} ) = \frac{1}{2} \\ \frac{3x}{2} = + - \frac{\pi}{3} + 2\pi \times n \\ 3x = + - \frac{2\pi}{3} + 4\pi \times n \\ x = + - \frac{2\pi}{9} + \frac{4\pi \times n}{3}$