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

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

Evaluate

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

Solution Steps

Evaluate trigonometric functions in the problem

$$2 \cdot 1 / 0.14054083470239145 \cdot 1 / 0.3057306814586604 \cdot 1 / \tan(45) \cdot 1 / 3.2708526184841404 \cdot 1 / 7.115369722384195$$

Multiply 2 and 1 to get 2.

$$\frac{1\times \frac{1\times \frac{\frac{\frac{2}{0.14054083470239145}\times 1}{0.3057306814586604}\times 1}{\tan(45)}}{3.2708526184841404}}{7.115369722384195}$$

Expand \frac{2}{0.14054083470239145} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{1\times \frac{1\times \frac{\frac{\frac{200000000000000000}{14054083470239145}\times 1}{0.3057306814586604}\times 1}{\tan(45)}}{3.2708526184841404}}{7.115369722384195}$$

Reduce the fraction \frac{200000000000000000}{14054083470239145} to lowest terms by extracting and canceling out 5.

$$\frac{1\times \frac{1\times \frac{\frac{\frac{40000000000000000}{2810816694047829}\times 1}{0.3057306814586604}\times 1}{\tan(45)}}{3.2708526184841404}}{7.115369722384195}$$

Multiply \frac{40000000000000000}{2810816694047829} and 1 to get \frac{40000000000000000}{2810816694047829}.

$$\frac{1\times \frac{1\times \frac{\frac{\frac{40000000000000000}{2810816694047829}}{0.3057306814586604}\times 1}{\tan(45)}}{3.2708526184841404}}{7.115369722384195}$$

Express \frac{\frac{40000000000000000}{2810816694047829}}{0.3057306814586604} as a single fraction.

$$\frac{1\times \frac{1\times \frac{\frac{40000000000000000}{2810816694047829\times 0.3057306814586604}\times 1}{\tan(45)}}{3.2708526184841404}}{7.115369722384195}$$

Multiply 2810816694047829 and 0.3057306814586604 to get 859352903326621.7159602038682716.

$$\frac{1\times \frac{1\times \frac{\frac{40000000000000000}{859352903326621.7159602038682716}\times 1}{\tan(45)}}{3.2708526184841404}}{7.115369722384195}$$

Expand \frac{40000000000000000}{859352903326621.7159602038682716} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{1\times \frac{1\times \frac{\frac{400000000000000000000000000000000}{8593529033266217159602038682716}\times 1}{\tan(45)}}{3.2708526184841404}}{7.115369722384195}$$

Reduce the fraction \frac{400000000000000000000000000000000}{8593529033266217159602038682716} to lowest terms by extracting and canceling out 4.

$$\frac{1\times \frac{1\times \frac{\frac{100000000000000000000000000000000}{2148382258316554289900509670679}\times 1}{\tan(45)}}{3.2708526184841404}}{7.115369722384195}$$

Multiply \frac{100000000000000000000000000000000}{2148382258316554289900509670679} and 1 to get \frac{100000000000000000000000000000000}{2148382258316554289900509670679}.

$$\frac{1\times \frac{1\times \frac{\frac{100000000000000000000000000000000}{2148382258316554289900509670679}}{\tan(45)}}{3.2708526184841404}}{7.115369722384195}$$

Get the value of \tan(45) from trigonometric values table.

$$\frac{1\times \frac{1\times \frac{\frac{100000000000000000000000000000000}{2148382258316554289900509670679}}{1}}{3.2708526184841404}}{7.115369722384195}$$

Anything divided by one gives itself.

$$\frac{1\times \frac{1\times \frac{100000000000000000000000000000000}{2148382258316554289900509670679}}{3.2708526184841404}}{7.115369722384195}$$

Multiply 1 and \frac{100000000000000000000000000000000}{2148382258316554289900509670679} to get \frac{100000000000000000000000000000000}{2148382258316554289900509670679}.

$$\frac{1\times \frac{\frac{100000000000000000000000000000000}{2148382258316554289900509670679}}{3.2708526184841404}}{7.115369722384195}$$

Express \frac{\frac{100000000000000000000000000000000}{2148382258316554289900509670679}}{3.2708526184841404} as a single fraction.

$$\frac{1\times \frac{100000000000000000000000000000000}{2148382258316554289900509670679\times 3.2708526184841404}}{7.115369722384195}$$

Multiply 2148382258316554289900509670679 and 3.2708526184841404 to get 7027041735119572517754492936408.8736997883993316.

$$\frac{1\times \frac{100000000000000000000000000000000}{7027041735119572517754492936408.8736997883993316}}{7.115369722384195}$$

Expand \frac{100000000000000000000000000000000}{7027041735119572517754492936408.8736997883993316} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{1\times \frac{1000000000000000000000000000000000000000000000000}{70270417351195725177544929364088736997883993316}}{7.115369722384195}$$

Reduce the fraction \frac{1000000000000000000000000000000000000000000000000}{70270417351195725177544929364088736997883993316} to lowest terms by extracting and canceling out 4.

$$\frac{1\times \frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}}{7.115369722384195}$$

Multiply 1 and \frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329} to get \frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}.

$$\frac{\frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}}{7.115369722384195}$$

Express \frac{\frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}}{7.115369722384195} as a single fraction.

$$\frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329\times 7.115369722384195}$$

Multiply 17567604337798931294386232341022184249470998329 and 7.115369722384195 to get 124999999999999761604594726581613146873250254105.004704741010155.

$$\frac{250000000000000000000000000000000000000000000000}{124999999999999761604594726581613146873250254105.004704741010155}$$

Expand \frac{250000000000000000000000000000000000000000000000}{124999999999999761604594726581613146873250254105.004704741010155} by multiplying both numerator and the denominator by 1000000000000000.

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

Reduce the fraction \frac{250000000000000000000000000000000000000000000000000000000000000}{124999999999999761604594726581613146873250254105004704741010155} to lowest terms by extracting and canceling out 5.

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