Etzel 1) cos²15-sin²15 = (cos(45-30))² - (sin(45-30))² = (cos45cos30+sin45sin30) - (sin45cos30-cos45sin30) = (√2/2 * √3/2 + √2/2 * 1/2)² - (√2/2 * √3/2 - √2/2 * 1/2)² = ((√6+√2)/4)²-((√6-√2)/4)²(6+2√12+2)/16 - (6-2√12+2)/16 = (4√12)/16 = (2√3)/4=√3/2
Но есть формула: cos²15-sin²15 = cos 30 = √3/2