Дано
$$sin^{2}{left (- a + 45 right )} – frac{1}{2} – sin{left (a right )} + cos{left (a right )}$$
Подстановка условия
$$sin^{2}{left (- a + 45 right )} – frac{1}{2} – sin{left (a right )} + cos{left (a right )}$$
sin(45 – (1/4))^2 – 1/2 – sin((1/4)) + cos((1/4))
$$sin^{2}{left (- (1/4) + 45 right )} – frac{1}{2} – sin{left ((1/4) right )} + cos{left ((1/4) right )}$$
sin(45 – 1/4)^2 – 1/2 – sin(1/4) + cos(1/4)
$$- sin{left (frac{1}{4} right )} + – frac{1}{2} + sin^{2}{left (- frac{1}{4} + 45 right )} + cos{left (frac{1}{4} right )}$$
-1/2 + sin(179/4)^2 – sin(1/4) + cos(1/4)
$$- frac{1}{2} – sin{left (frac{1}{4} right )} + sin^{2}{left (frac{179}{4} right )} + cos{left (frac{1}{4} right )}$$
Степени
$$- sin{left (a right )} + sin^{2}{left (a – 45 right )} + cos{left (a right )} – frac{1}{2}$$
Численный ответ
-0.5 + sin(45 – a)^2 – sin(a) + cos(a)
Рациональный знаменатель
$$frac{1}{2} left(- 2 sin{left (a right )} + 2 sin^{2}{left (a – 45 right )} + 2 cos{left (a right )} – 1right)$$
Объединение рациональных выражений
$$frac{1}{2} left(- 2 sin{left (a right )} + 2 sin^{2}{left (a – 45 right )} + 2 cos{left (a right )} – 1right)$$
Общее упрощение
cos(-90 + 2*a) ___ / pi
– ————– + / 2 *cos|a + –|
2 4 /
$$sqrt{2} cos{left (a + frac{pi}{4} right )} – frac{1}{2} cos{left (2 a – 90 right )}$$
Соберем выражение
$$- sin{left (a right )} + cos{left (a right )} – frac{1}{2} cos{left (2 a – 90 right )}$$
1 2
– – + sin (45 – a) – sin(a) + cos(a)
2
$$- sin{left (a right )} + sin^{2}{left (- a + 45 right )} + cos{left (a right )} – frac{1}{2}$$
Общий знаменатель
1 2
– – + sin (45 – a) – sin(a) + cos(a)
2
$$- sin{left (a right )} + sin^{2}{left (- a + 45 right )} + cos{left (a right )} – frac{1}{2}$$
Комбинаторика
2
-1 – 2*sin(a) + 2*sin (-45 + a) + 2*cos(a)
——————————————
2
$$frac{1}{2} left(- 2 sin{left (a right )} + 2 sin^{2}{left (a – 45 right )} + 2 cos{left (a right )} – 1right)$$
Тригонометрическая часть
cos(-90 + 2*a) ___ / pi
– ————– + / 2 *cos|a + –|
2 4 /
$$sqrt{2} cos{left (a + frac{pi}{4} right )} – frac{1}{2} cos{left (2 a – 90 right )}$$
Раскрыть выражение
1 2
– – + (cos(45)*sin(a) – cos(a)*sin(45)) – sin(a) + cos(a)
2
$$left(sin{left (a right )} cos{left (45 right )} – sin{left (45 right )} cos{left (a right )}right)^{2} – sin{left (a right )} + cos{left (a right )} – frac{1}{2}$$
