Дано
$$left(sqrt{frac{sin{left (a right )} + 1}{- sin{left (a right )} + 1}} – sqrt{frac{- sin{left (a right )} + 1}{sin{left (a right )} + 1}}right) cot{left (a right )}$$
Подстановка условия
/ _______________________ _______________________
| / 1 / 1 |
| / (1 + sin(a))*——– – / (1-sin(a))*———- |*cot(a)
/ 1-sin(a) / 1 + sin(a) /
(sqrt((1 + sin((-1/3)))*1/(1 – sin((-1/3)))) – sqrt((1 – sin((-1/3)))*1/(1 + sin((-1/3)))))*cot((-1/3))
/ _________________________________ _________________________________
| / 1 / 1 |
| / (1 + sin((-1/3)))*————- – / (1-sin((-1/3)))*————— |*cot((-1/3))
/ 1-sin((-1/3)) / 1 + sin((-1/3)) /
(sqrt((1 + sin(-1/3))*1/(1 – sin(-1/3))) – sqrt((1 – sin(-1/3))*1/(1 + sin(-1/3))))*cot(-1/3)
/ _____________________________ _____________________________
| / 1 / 1 |
| / (1 + sin(-1/3))*———– – / (1-sin(-1/3))*————- |*cot(-1/3)
/ 1-sin(-1/3) / 1 + sin(-1/3) /
-(sqrt(1 – sin(1/3))/sqrt(1 + sin(1/3)) – sqrt(1 + sin(1/3))/sqrt(1 – sin(1/3)))*cot(1/3)
$$-1 left(frac{-1 sqrt{sin{left (frac{1}{3} right )} + 1}}{sqrt{-1 sin{left (frac{1}{3} right )} + 1}} + frac{sqrt{-1 sin{left (frac{1}{3} right )} + 1}}{sqrt{sin{left (frac{1}{3} right )} + 1}}right) cot{left (frac{1}{3} right )}$$
Численный ответ
(((1.0 + sin(a))/(1.0 – sin(a)))^0.5 – ((1.0 – sin(a))/(1.0 + sin(a)))^0.5)*cot(a)
Общее упрощение
/ ________________ ____________
| / -(1 + sin(a)) / 1 – sin(a) |
| / ————– – / ———- |*cot(a)
/ -1 + sin(a) / 1 + sin(a) /
$$left(- sqrt{frac{- sin{left (a right )} + 1}{sin{left (a right )} + 1}} + sqrt{- frac{sin{left (a right )} + 1}{sin{left (a right )} – 1}}right) cot{left (a right )}$$
Соберем выражение
$$frac{2 sin{left (a right )} cot{left (a right )}}{sqrt{- sin{left (a right )} + 1} sqrt{sin{left (a right )} + 1}}$$
Общий знаменатель
_________________________ _________________________
/ 1 sin(a) / 1 sin(a)
/ ———- + ———- *cot(a) – / ———- – ———- *cot(a)
/ 1 – sin(a) 1 – sin(a) / 1 + sin(a) 1 + sin(a)
$$sqrt{frac{sin{left (a right )}}{- sin{left (a right )} + 1} + frac{1}{- sin{left (a right )} + 1}} cot{left (a right )} – sqrt{- frac{sin{left (a right )}}{sin{left (a right )} + 1} + frac{1}{sin{left (a right )} + 1}} cot{left (a right )}$$
Комбинаторика
/ _________________________ _________________________
| / 1 sin(a) / 1 sin(a) |
-| / ———- – ———- – / ———- + ———- |*cot(a)
/ 1 + sin(a) 1 + sin(a) / 1 – sin(a) 1 – sin(a) /
$$- left(- sqrt{frac{sin{left (a right )}}{- sin{left (a right )} + 1} + frac{1}{- sin{left (a right )} + 1}} + sqrt{- frac{sin{left (a right )}}{sin{left (a right )} + 1} + frac{1}{sin{left (a right )} + 1}}right) cot{left (a right )}$$
Раскрыть выражение
/ ____________ ____________
| / 1 ____________ / 1 ____________|
| / ———- */ 1 + sin(a) – / ———- */ 1 – sin(a) |*cot(a)
/ 1 – sin(a) / 1 + sin(a) /
$$left(- sqrt{- sin{left (a right )} + 1} sqrt{frac{1}{sin{left (a right )} + 1}} + sqrt{sin{left (a right )} + 1} sqrt{frac{1}{- sin{left (a right )} + 1}}right) cot{left (a right )}$$
/ ____________ ____________
|/ 1 + sin(a) / 1 – sin(a) |
|————– – ————–|*cot(a)
| ____________ ____________|
/ 1 – sin(a) / 1 + sin(a) /
$$left(- frac{sqrt{- sin{left (a right )} + 1}}{sqrt{sin{left (a right )} + 1}} + frac{sqrt{sin{left (a right )} + 1}}{sqrt{- sin{left (a right )} + 1}}right) cot{left (a right )}$$
