Дано
$$sqrt{sin^{4}{left (x right )} + 2 – cos{left (2 x right )}} + sqrt{cos^{4}{left (x right )} + 2 + cos{left (2 x right )}}$$
Подстановка условия
$$sqrt{sin^{4}{left (x right )} + 2 – cos{left (2 x right )}} + sqrt{cos^{4}{left (x right )} + 2 + cos{left (2 x right )}}$$
sqrt(2 + sin((1))^4 – cos(2*(1))) + sqrt(2 + cos((1))^4 + cos(2*(1)))
$$sqrt{sin^{4}{left ((1) right )} + 2 – cos{left (2 (1) right )}} + sqrt{cos^{4}{left ((1) right )} + 2 + cos{left (2 (1) right )}}$$
sqrt(2 + sin(1)^4 – cos(2)) + sqrt(2 + cos(1)^4 + cos(2))
$$sqrt{cos{left (2 right )} + cos^{4}{left (1 right )} + 2} + sqrt{- cos{left (2 right )} + sin^{4}{left (1 right )} + 2}$$
sqrt(2 + cos(1)^4 + cos(2)) + sqrt(2 + sin(1)^4 – cos(2))
$$sqrt{cos{left (2 right )} + cos^{4}{left (1 right )} + 2} + sqrt{- cos{left (2 right )} + sin^{4}{left (1 right )} + 2}$$
Степени
$$sqrt{sin^{4}{left (x right )} – cos{left (2 x right )} + 2} + sqrt{cos^{4}{left (x right )} + cos{left (2 x right )} + 2}$$
Численный ответ
(2.0 + cos(x)^4 + cos(2*x))^0.5 + (2.0 + sin(x)^4 – cos(2*x))^0.5
Рациональный знаменатель
$$sqrt{sin^{4}{left (x right )} – cos{left (2 x right )} + 2} + sqrt{cos^{4}{left (x right )} + cos{left (2 x right )} + 2}$$
Объединение рациональных выражений
$$sqrt{sin^{4}{left (x right )} – cos{left (2 x right )} + 2} + sqrt{cos^{4}{left (x right )} + cos{left (2 x right )} + 2}$$
Общее упрощение
________________ _________________
/ 2 / 2
/ / 2 / / 2
/ 1 + sin (x)/ + / -2 + sin (x)/
$$sqrt{left(sin^{2}{left (x right )} – 2right)^{2}} + sqrt{left(sin^{2}{left (x right )} + 1right)^{2}}$$
Соберем выражение
$$sqrt{- frac{3}{2} cos{left (2 x right )} + frac{1}{8} cos{left (4 x right )} + frac{19}{8}} + sqrt{frac{3}{2} cos{left (2 x right )} + frac{1}{8} cos{left (4 x right )} + frac{19}{8}}$$
Общий знаменатель
________________________ ________________________
/ 4 / 4
/ 2 + cos (x) + cos(2*x) + / 2 + sin (x) – cos(2*x)
$$sqrt{sin^{4}{left (x right )} – cos{left (2 x right )} + 2} + sqrt{cos^{4}{left (x right )} + cos{left (2 x right )} + 2}$$
Тригонометрическая часть
________________ _________________
/ 2 / 2
/ / 2 / / 2
/ 1 + sin (x)/ + / -2 + sin (x)/
$$sqrt{left(sin^{2}{left (x right )} – 2right)^{2}} + sqrt{left(sin^{2}{left (x right )} + 1right)^{2}}$$
Комбинаторика
________________________ ________________________
/ 4 / 4
/ 2 + cos (x) + cos(2*x) + / 2 + sin (x) – cos(2*x)
$$sqrt{sin^{4}{left (x right )} – cos{left (2 x right )} + 2} + sqrt{cos^{4}{left (x right )} + cos{left (2 x right )} + 2}$$
Раскрыть выражение
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/ 2 4 2 / 2 4 2
/ 2 + cos (x) + cos (x) – sin (x) + / 2 + sin (x) + sin (x) – cos (x)
$$sqrt{- sin^{2}{left (x right )} + cos^{4}{left (x right )} + cos^{2}{left (x right )} + 2} + sqrt{sin^{4}{left (x right )} + sin^{2}{left (x right )} – cos^{2}{left (x right )} + 2}$$
