Решете (2)cos80^circ/sin20^circ+cos59^circcsc31^circ=2

$$( 2 ) \frac { \cos 80 ^ { \circ } } { \sin 20 ^ { \circ } } + \cos 59 ^ { \circ } \csc 31 ^ { \circ } = 2$$

Проверка

Стъпки на решението

Evaluate trigonometric functions in the problem

$${(2)} \frac{0,17364817766693041}{0,3420201433256687} + 0,5150380749100543 \cdot 1,9416040264103567 = 2$$

Разширете \frac{0,17364817766693041}{0,3420201433256687}, като умножите числителя и знаменателя по 100000000000000000.

$$2\times \frac{17364817766693041}{34202014332566870}+0,5150380749100543\times 1,9416040264103567=2$$

Изразете 2\times \frac{17364817766693041}{34202014332566870} като една дроб.

$$\frac{2\times 17364817766693041}{34202014332566870}+0,5150380749100543\times 1,9416040264103567=2$$

Умножете 2 по 17364817766693041, за да получите 34729635533386082.

$$\frac{34729635533386082}{34202014332566870}+0,5150380749100543\times 1,9416040264103567=2$$

Намаляване на дробта \frac{34729635533386082}{34202014332566870} до най-малките членове чрез извличане на корен и съкращаване на 2.

$$\frac{17364817766693041}{17101007166283435}+0,5150380749100543\times 1,9416040264103567=2$$

Умножете 0,5150380749100543 по 1,9416040264103567, за да получите 1,00000000000000034155305447936881.

$$\frac{17364817766693041}{17101007166283435}+1,00000000000000034155305447936881=2$$

Преобразуване на десетично число 1,00000000000000034155305447936881 в дроб \frac{100000000000000034155305447936881}{10000000000}. Намаляване на дробта \frac{100000000000000034155305447936881}{10000000000} до най-малките членове чрез извличане на корен и съкращаване на 1.

$$\frac{17364817766693041}{17101007166283435}+\frac{100000000000000034155305447936881}{100000000000000000000000000000000}=2$$

Най-малко общо кратно на 17101007166283435 и 100000000000000000000000000000000 е 342020143325668700000000000000000000000000000000. Преобразувайте \frac{17364817766693041}{17101007166283435} и \frac{100000000000000034155305447936881}{100000000000000000000000000000000} в дроби със знаменател 342020143325668700000000000000000000000000000000.

$$\frac{347296355333860820000000000000000000000000000000}{342020143325668700000000000000000000000000000000}+\frac{342020143325668816818024646353650179265047173247}{342020143325668700000000000000000000000000000000}=2$$

Тъй като \frac{347296355333860820000000000000000000000000000000}{342020143325668700000000000000000000000000000000} и \frac{342020143325668816818024646353650179265047173247}{342020143325668700000000000000000000000000000000} имат един и същ знаменател, съберете ги, като съберете техните числители.

$$\frac{347296355333860820000000000000000000000000000000+342020143325668816818024646353650179265047173247}{342020143325668700000000000000000000000000000000}=2$$

Съберете 347296355333860820000000000000000000000000000000 и 342020143325668816818024646353650179265047173247, за да се получи 689316498659529636818024646353650179265047173247.

$$\frac{689316498659529636818024646353650179265047173247}{342020143325668700000000000000000000000000000000}=2$$

Преобразуване на 2 в дроб \frac{684040286651337400000000000000000000000000000000}{342020143325668700000000000000000000000000000000}.

$$\frac{689316498659529636818024646353650179265047173247}{342020143325668700000000000000000000000000000000}=\frac{684040286651337400000000000000000000000000000000}{342020143325668700000000000000000000000000000000}$$

Сравняване на \frac{689316498659529636818024646353650179265047173247}{342020143325668700000000000000000000000000000000} и \frac{684040286651337400000000000000000000000000000000}{342020143325668700000000000000000000000000000000}.

$$\text{false}$$