Наверное, Вы это имели в виду
![1+\frac{\cot(x)\cot(y)*\cos(x+y)}{\cos x\cos y}](https://tex.z-dn.net/?f=1%2B%5Cfrac%7B%5Ccot%28x%29%5Ccot%28y%29%2A%5Ccos%28x%2By%29%7D%7B%5Ccos+x%5Ccos+y%7D)
По формуле котангенса
![\cot\alpha=\frac{\cos\alpha}{\sin\alpha}](https://tex.z-dn.net/?f=%5Ccot%5Calpha%3D%5Cfrac%7B%5Ccos%5Calpha%7D%7B%5Csin%5Calpha%7D)
![1+\frac{\cot(x)\cot(y)*\cos(x+y)}{\cos x\cos y}=1+\frac{\cos(x)\cos(y)*\cos(x+y)}{\cos x\cos y\sin x\sin y}](https://tex.z-dn.net/?f=1%2B%5Cfrac%7B%5Ccot%28x%29%5Ccot%28y%29%2A%5Ccos%28x%2By%29%7D%7B%5Ccos+x%5Ccos+y%7D%3D1%2B%5Cfrac%7B%5Ccos%28x%29%5Ccos%28y%29%2A%5Ccos%28x%2By%29%7D%7B%5Ccos+x%5Ccos+y%5Csin+x%5Csin+y%7D)
Сокращаем числитель и знаменатель
![1+\frac{\cos(x+y)}{\sin x\sin y}](https://tex.z-dn.net/?f=1%2B%5Cfrac%7B%5Ccos%28x%2By%29%7D%7B%5Csin+x%5Csin+y%7D)
Разложим по формуле косинуса суммы
![1+\frac{\cos(x+y)}{\sin x\sin y}=1+\frac{\cos x\cos y -\sin x\sin y}{\sin x\sin y}](https://tex.z-dn.net/?f=1%2B%5Cfrac%7B%5Ccos%28x%2By%29%7D%7B%5Csin+x%5Csin+y%7D%3D1%2B%5Cfrac%7B%5Ccos+x%5Ccos+y+-%5Csin+x%5Csin+y%7D%7B%5Csin+x%5Csin+y%7D)
Снова сокращаем насколько возможно
![1+\frac{\cos x\cos y -\sin x\sin y}{\sin x\sin y}=1+\frac{\cos x\cos y}{\sin x\sin y}-1](https://tex.z-dn.net/?f=1%2B%5Cfrac%7B%5Ccos+x%5Ccos+y+-%5Csin+x%5Csin+y%7D%7B%5Csin+x%5Csin+y%7D%3D1%2B%5Cfrac%7B%5Ccos+x%5Ccos+y%7D%7B%5Csin+x%5Csin+y%7D-1)
Снова по формуле котангенса
![\frac{\cos x\cos y}{\sin x\sin y}=\cot x\cot y](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ccos+x%5Ccos+y%7D%7B%5Csin+x%5Csin+y%7D%3D%5Ccot+x%5Ccot+y)
167.
1) 1 - (√x)^3
2) (√a)^3 + 8
169.
2)(√a+√b)/(a√a + b√b) =(√a+√b)/((√a)^3 + (√b)^3) = (√a+√b)/(√a+√b)(a - √ab + b) = = 1/(a - √ab + b) = (a - √ab + b)^ -1
Ответ во вложении.
Использовал свойства корней.