Question

Sin²2x=sin3x-cos(╥/2+x) нужно решение ,

Answer 1

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