Sin5x*sin(5x+2pi/9)=sin13pi/6*cos2p i/9

1) sin 13pi/6 = sin(12pi/6 + pi/6) = sin(2pi + pi/6) = sin pi/6 = 1/2 2) подставляем sin 5x*(sin 5x*cos 2pi/9 + cos 5x*sin 2pi/9) = 1/2*cos 2pi/9 sin 5x*cos 5x*sin 2pi/9 = 1/2*cos 2pi/9 - sin^2 5x*cos 2pi/9 умножаем все на 2 и делим на cos 2pi/9 2sin 5x*cos 5x*tg 2pi/9 = 1 - 2sin^2 5x sin 10x*tg 2pi/9 = cos 10x tg 10x*tg 2pi/9 = 1 tg 10x = ctg 2pi/9 = ctg 4pi/18 = tg (pi/2 - 4pi/18) = tg 5pi/18 x = 1/10*(5pi/18 + pi*k) = pi/36 + pi/10*k

5379^2 - 5378 * 5380 =  5379^2 - 5378 * (5379 + 1)=

= 5379^2 - 5378 * 5379 - 5378 = 5379 * (5379 - 5378) - 5378 =

= 5379 - 5378 = 1