<span>а) cos x + sin y = cosx+cos(p/2-y)=2cos((x-y)/2+p/4)cos((x+y)/2-p/4)
б) cos x - sin x= cosx+cos(p/2+x)=2cos(x+p/4)cos(p/4)=</span>√2cos(x+p/4)
<span>в) sin 2x - cos x=cos(p/2-2x)-cosx=-2sin(p/4-x/2)sin(p/4-3x/2)</span>
1) a² + 10a + 25 = a² + 2 * a * 5 + 5² = (a + 5)²
2) 4x² - 4x + 1 = (2x)² - 2 * 2x * 1 + 1² = (2x - 1)²
3) 64n² - 80nq + 25q² = (8n)² - 2 * 8n * 5q + (5q)² = (8n - 5q)²
4) m⁸ - 6m⁴n⁵ + 9n¹⁰ = (m⁴)² - 2 * m⁴ * (3n⁵) + (3n⁵)² = (m⁴ - 3n⁵)²
5) 36x¹² + y⁶ + 12x⁶y³ = 36x¹² + 12x⁶y³ + y⁶ = (6x⁶)² + 2 * 6x⁶ * y³ + (y³)² =
= (6x⁶ + y³)²