4. Найдите значение: 3ctga + 2tg²a – √2cosa, если sina=√2/2; 0<a<П/2 дайте полный ответ

3ctga + 2tg²a – √2cosa = 3 * cot(a) + 2 * tan²(a) - √2 * cos(a) Since sin(a) = √2/2 and 0 <a<π/2: cot(a) = cos(a)/sin(a) = cos(a)/√2 tan(a) = sin(a)/cos(a) = √2

Substitute in the equation: 3 * (cos(a)/√2) + 2 * (√2)² - √2 * cos(a) = 3 * (cos(a)/√2) + 2 * 2 - √2 * cos(a) = 3 * (cos(a)/√2) + 4 - √2 * cos(a)

= 3 * (√2/2) + 4 - √2 * (√2/2) = 3√2/2 + 4 - 2 = 3√2/2 + 2

Ответ: 3√2/2 + 2