Дано
$$frac{- tan^{2}{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )} – 1}{2 sqrt{- x^{2} + 1} tan{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )}}$$
Подстановка условия
$$frac{- tan^{2}{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )} – 1}{2 sqrt{- x^{2} + 1} tan{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )}}$$
(-1 – tan(pi/4 + acos((-1/4))/2)^2)/((2*sqrt(1 – (-1/4)^2))*tan(pi/4 + acos((-1/4))/2))
$$frac{- tan^{2}{left (frac{1}{2} {acos}{left ((-1/4) right )} + frac{pi}{4} right )} – 1}{2 sqrt{- (-1/4)^{2} + 1} tan{left (frac{1}{2} {acos}{left ((-1/4) right )} + frac{pi}{4} right )}}$$
(-1 – tan(pi/4 + acos(-1/4)/2)^2)/((2*sqrt(1 – (-1/4)^2))*tan(pi/4 + acos(-1/4)/2))
$$frac{- tan^{2}{left (frac{pi}{4} + frac{1}{2} {acos}{left (- frac{1}{4} right )} right )} – 1}{2 sqrt{- frac{1}{16} + 1} tan{left (frac{pi}{4} + frac{1}{2} {acos}{left (- frac{1}{4} right )} right )}}$$
2*sqrt(15)*(-1 – tan(acos(-1/4)/2 + pi/4)^2)/(15*tan(acos(-1/4)/2 + pi/4))
$$frac{2 sqrt{15} left(- tan^{2}{left (frac{pi}{4} + frac{1}{2} {acos}{left (- frac{1}{4} right )} right )} – 1right)}{15 tan{left (frac{pi}{4} + frac{1}{2} {acos}{left (- frac{1}{4} right )} right )}}$$
Степени
$$frac{- frac{1}{2} tan^{2}{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )} – frac{1}{2}}{sqrt{- x^{2} + 1} tan{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )}}$$
Численный ответ
0.5*(1.0 – x^2)^(-0.5)*(-1.0 – tan(pi/4 + acos(x)/2)^2)/tan(pi/4 + acos(x)/2)
Рациональный знаменатель
$$frac{sqrt{- x^{2} + 1} tan^{2}{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )} + sqrt{- x^{2} + 1}}{2 left(x^{2} – 1right) tan{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )}}$$
Объединение рациональных выражений
$$frac{- tan^{2}{left (frac{1}{4} left(2 {acos}{left (x right )} + piright) right )} – 1}{2 sqrt{- x^{2} + 1} tan{left (frac{1}{4} left(2 {acos}{left (x right )} + piright) right )}}$$
Общее упрощение
-1
————-
________
/ 2
x*/ 1 – x
$$- frac{1}{x sqrt{- x^{2} + 1}}$$
Соберем выражение
$$- frac{sec^{2}{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )}}{2 sqrt{- x^{2} + 1}} cot{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )}$$
Общий знаменатель
/ 2/acos(x) pi
-|1 + tan |——- + –||
2 4 //
——————————-
________
/ 2 /acos(x) pi
2*/ 1 – x *tan|——- + –|
2 4 /
$$- frac{tan^{2}{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )} + 1}{2 sqrt{- x^{2} + 1} tan{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )}}$$
Комбинаторика
/ 2/acos(x) pi
-|1 + tan |——- + –||
2 4 //
—————————————–
___________________ /acos(x) pi
2*/ -(1 + x)*(-1 + x) *tan|——- + –|
2 4 /
$$- frac{tan^{2}{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )} + 1}{2 sqrt{- left(x – 1right) left(x + 1right)} tan{left (frac{1}{2} {acos}{left (x right )} + frac{pi}{4} right )}}$$
Раскрыть выражение
/ 2
| / /acos(x) |
| |1 + tan|——-|| |
/ /acos(x) | 2 // |
|1 – tan|——-||*|-1 – ——————-|
2 // | 2|
| / /acos(x) |
| |1 – tan|——-|| |
2 // /
———————————————
________
/ 2 / /acos(x)
2*/ 1 – x *|1 + tan|——-||
2 //
$$frac{1}{2 sqrt{- x^{2} + 1} left(tan{left (frac{1}{2} {acos}{left (x right )} right )} + 1right)} left(-1 – frac{left(tan{left (frac{1}{2} {acos}{left (x right )} right )} + 1right)^{2}}{left(- tan{left (frac{1}{2} {acos}{left (x right )} right )} + 1right)^{2}}right) left(- tan{left (frac{1}{2} {acos}{left (x right )} right )} + 1right)$$
