∠BOF = ∠AOE = 40° как вертикальные
∠COE = ∠DOF = 80° как вертикальные
∠EOF = ∠COE+∠COB+∠BOF = 180°, т.к. EOF - развёрнутый угол.
∠COE+∠COB+∠BOF = 180°
80°+∠COB+40° = 180°
∠COB+120° = 180°
∠COB = 180°-120°
∠COB = 60°
Sin^2 x+sin^2 2x=1
<span>sin^2 2x=1-sin^2 x </span>
<span>sin^2 2x=cos^2 x </span>
<span>4sin^2 x * cos^2 x=cos^2 x </span>
<span>cos^2 x*(4sin^2 x-1)=0 </span>
<span>1) cosx=0 </span>
<span>x=пи/2+пи*n, n - целое </span>
<span>2) 4sin^2 x-1=0 </span>
<span>2(1-cos2x)-1=0 </span>
<span>-2cos2x+1=0 </span>
<span>cos2x=1/2 </span>
<span>2x=+-пи/3+2пи*n, </span>
<span>x=+-пи/6+пи*n, n - целое </span>
<span>Ответ: x=пи/2+пи*n, x=+-пи/6+пи*n, n - целое</span>
550 mod 546 = 4
546 mod 4 = 2
4 mod 2 = 0
НОД(550, 546) = 2.
НОК(550, 546) = 550 * 546 / НОД(550, 546) = 150150