Question

СРОЧНО! подробное решение$sin ^{2} 7x-sin^{2} 5x = 0$

Answer 1

$sin^2(7x)-sin^2(5x)=0\\(sin(7x)-sin(5x))(sin(7x)+sin(5x))=0\\sin(7x)-sin(5x)=0\\2cos(\frac{7x+5x}{2} )sin(\frac{7x-5x}{2} )=0\\2cos(6x)sin(x)=0\\cos(6x)=0\\6x=\frac{\pi}{2} +k\pi\\x=\frac{\pi}{12} +\frac{k\pi}{6} \\sin(x)=0\\x=\pi k..................................................\\sin(7x)+sin(5x)=0\\2sin(6x)cos(x)=0\\sin(6x)=0\\6x=k\pi\\x=\frac{k\pi}{6} \\cos(x)=0\\x=\frac{\pi}{2} +k \pi$
везде k∈Z