Решете 2*1divtan(8^{circ})*1divtan(17^circ)*1divtan(45^circ)*1divtan(73^circ)*1divtan(82^circ)

$$2 \times 1 \div \tan ( 8 ^ { \circ } ) \times 1 \div \tan ( 17 ^ { \circ } ) \times 1 \div \tan ( 45 ^ { \circ } ) \times 1 \div \tan ( 73 ^ { \circ } ) \times 1 \div \tan ( 82 ^ { \circ } )$$

Изчисляване

$$\frac{50000000000000000000000000000000000000000000000000000000000000}{24999999999999952320918945316322629374650050821000940948202031}\approx 2$$

Стъпки на решението

Evaluate trigonometric functions in the problem

$$2 \cdot 1 / 0,14054083470239145 \cdot 1 / 0,3057306814586604 \cdot 1 / \tan(45) \cdot 1 / 3,2708526184841404 \cdot 1 / 7,115369722384195$$

Умножете 2 по 1, за да получите 2.

$$\frac{1\times \frac{1\times \frac{\frac{\frac{2}{0,14054083470239145}\times 1}{0,3057306814586604}\times 1}{\tan(45)}}{3,2708526184841404}}{7,115369722384195}$$

Разширете \frac{2}{0,14054083470239145}, като умножите числителя и знаменателя по 100000000000000000.

$$\frac{1\times \frac{1\times \frac{\frac{\frac{200000000000000000}{14054083470239145}\times 1}{0,3057306814586604}\times 1}{\tan(45)}}{3,2708526184841404}}{7,115369722384195}$$

Намаляване на дробта \frac{200000000000000000}{14054083470239145} до най-малките членове чрез извличане на корен и съкращаване на 5.

$$\frac{1\times \frac{1\times \frac{\frac{\frac{40000000000000000}{2810816694047829}\times 1}{0,3057306814586604}\times 1}{\tan(45)}}{3,2708526184841404}}{7,115369722384195}$$

Умножете \frac{40000000000000000}{2810816694047829} по 1, за да получите \frac{40000000000000000}{2810816694047829}.

$$\frac{1\times \frac{1\times \frac{\frac{\frac{40000000000000000}{2810816694047829}}{0,3057306814586604}\times 1}{\tan(45)}}{3,2708526184841404}}{7,115369722384195}$$

Изразете \frac{\frac{40000000000000000}{2810816694047829}}{0,3057306814586604} като една дроб.

$$\frac{1\times \frac{1\times \frac{\frac{40000000000000000}{2810816694047829\times 0,3057306814586604}\times 1}{\tan(45)}}{3,2708526184841404}}{7,115369722384195}$$

Умножете 2810816694047829 по 0,3057306814586604, за да получите 859352903326621,7159602038682716.

$$\frac{1\times \frac{1\times \frac{\frac{40000000000000000}{859352903326621,7159602038682716}\times 1}{\tan(45)}}{3,2708526184841404}}{7,115369722384195}$$

Разширете \frac{40000000000000000}{859352903326621,7159602038682716}, като умножите числителя и знаменателя по 10000000000000000.

$$\frac{1\times \frac{1\times \frac{\frac{400000000000000000000000000000000}{8593529033266217159602038682716}\times 1}{\tan(45)}}{3,2708526184841404}}{7,115369722384195}$$

Намаляване на дробта \frac{400000000000000000000000000000000}{8593529033266217159602038682716} до най-малките членове чрез извличане на корен и съкращаване на 4.

$$\frac{1\times \frac{1\times \frac{\frac{100000000000000000000000000000000}{2148382258316554289900509670679}\times 1}{\tan(45)}}{3,2708526184841404}}{7,115369722384195}$$

Умножете \frac{100000000000000000000000000000000}{2148382258316554289900509670679} по 1, за да получите \frac{100000000000000000000000000000000}{2148382258316554289900509670679}.

$$\frac{1\times \frac{1\times \frac{\frac{100000000000000000000000000000000}{2148382258316554289900509670679}}{\tan(45)}}{3,2708526184841404}}{7,115369722384195}$$

Получете стойността на \tan(45) от таблицата с тригонометрични стойности.

$$\frac{1\times \frac{1\times \frac{\frac{100000000000000000000000000000000}{2148382258316554289900509670679}}{1}}{3,2708526184841404}}{7,115369722384195}$$

Всяко число, разделено на едно, дава себе си.

$$\frac{1\times \frac{1\times \frac{100000000000000000000000000000000}{2148382258316554289900509670679}}{3,2708526184841404}}{7,115369722384195}$$

Умножете 1 по \frac{100000000000000000000000000000000}{2148382258316554289900509670679}, за да получите \frac{100000000000000000000000000000000}{2148382258316554289900509670679}.

$$\frac{1\times \frac{\frac{100000000000000000000000000000000}{2148382258316554289900509670679}}{3,2708526184841404}}{7,115369722384195}$$

Изразете \frac{\frac{100000000000000000000000000000000}{2148382258316554289900509670679}}{3,2708526184841404} като една дроб.

$$\frac{1\times \frac{100000000000000000000000000000000}{2148382258316554289900509670679\times 3,2708526184841404}}{7,115369722384195}$$

Умножете 2148382258316554289900509670679 по 3,2708526184841404, за да получите 7027041735119572517754492936408,8736997883993316.

$$\frac{1\times \frac{100000000000000000000000000000000}{7027041735119572517754492936408,8736997883993316}}{7,115369722384195}$$

Разширете \frac{100000000000000000000000000000000}{7027041735119572517754492936408,8736997883993316}, като умножите числителя и знаменателя по 10000000000000000.

$$\frac{1\times \frac{1000000000000000000000000000000000000000000000000}{70270417351195725177544929364088736997883993316}}{7,115369722384195}$$

Намаляване на дробта \frac{1000000000000000000000000000000000000000000000000}{70270417351195725177544929364088736997883993316} до най-малките членове чрез извличане на корен и съкращаване на 4.

$$\frac{1\times \frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}}{7,115369722384195}$$

Умножете 1 по \frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}, за да получите \frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}.

$$\frac{\frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}}{7,115369722384195}$$

Изразете \frac{\frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}}{7,115369722384195} като една дроб.

$$\frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329\times 7,115369722384195}$$

Умножете 17567604337798931294386232341022184249470998329 по 7,115369722384195, за да получите 124999999999999761604594726581613146873250254105,004704741010155.

$$\frac{250000000000000000000000000000000000000000000000}{124999999999999761604594726581613146873250254105,004704741010155}$$

Разширете \frac{250000000000000000000000000000000000000000000000}{124999999999999761604594726581613146873250254105,004704741010155}, като умножите числителя и знаменателя по 1000000000000000.

$$\frac{250000000000000000000000000000000000000000000000000000000000000}{124999999999999761604594726581613146873250254105004704741010155}$$

Намаляване на дробта \frac{250000000000000000000000000000000000000000000000000000000000000}{124999999999999761604594726581613146873250254105004704741010155} до най-малките членове чрез извличане на корен и съкращаване на 5.

$$\frac{50000000000000000000000000000000000000000000000000000000000000}{24999999999999952320918945316322629374650050821000940948202031}$$