Вычислить (9—10). 9.6 cos π/12. 10.6 tg π/8

9. cos(π/12) = cos(15°) = cos(45° - 30°) = cos45°cos30° + sin45°sin30° = (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4

10. tg(π/8) = tg(22.5°) Используем формулу tg(x/2) = sin(x) / (1 + cos(x)).

tg(π/8) = sin(π/4) / (1 + cos(π/4)) = (√2/2) / (1 + √2/2) = √2 / (2 + √2) = √2(2 - √2) / (4 - 2) = (2√2 - 2) / 2 = √2 - 1

Ответ: 9) (√6 + √2)/4; 10) √2 - 1