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

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

I-evaluate

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

Mga Hakbang ng Solution

Evaluate trigonometric functions in the problem

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

I-multiply ang 2 at 1 para makuha ang 2.

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

I-expand ang \frac{2}{0.14054083470239145} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 100000000000000000.

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

Bawasan ang fraction \frac{200000000000000000}{14054083470239145} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 5.

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

I-multiply ang \frac{40000000000000000}{2810816694047829} at 1 para makuha ang \frac{40000000000000000}{2810816694047829}.

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

Ipakita ang \frac{\frac{40000000000000000}{2810816694047829}}{0.3057306814586604} bilang isang single fraction.

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

I-multiply ang 2810816694047829 at 0.3057306814586604 para makuha ang 859352903326621.7159602038682716.

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

I-expand ang \frac{40000000000000000}{859352903326621.7159602038682716} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 10000000000000000.

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

Bawasan ang fraction \frac{400000000000000000000000000000000}{8593529033266217159602038682716} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 4.

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

I-multiply ang \frac{100000000000000000000000000000000}{2148382258316554289900509670679} at 1 para makuha ang \frac{100000000000000000000000000000000}{2148382258316554289900509670679}.

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

Kunin ang halaga ng \tan(45) mula sa talahanayan ng trigonometric values.

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

Ang anumang numero na idi-divide sa isa, ang sagot ay ang numerong ito pa rin.

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

I-multiply ang 1 at \frac{100000000000000000000000000000000}{2148382258316554289900509670679} para makuha ang \frac{100000000000000000000000000000000}{2148382258316554289900509670679}.

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

Ipakita ang \frac{\frac{100000000000000000000000000000000}{2148382258316554289900509670679}}{3.2708526184841404} bilang isang single fraction.

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

I-multiply ang 2148382258316554289900509670679 at 3.2708526184841404 para makuha ang 7027041735119572517754492936408.8736997883993316.

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

I-expand ang \frac{100000000000000000000000000000000}{7027041735119572517754492936408.8736997883993316} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 10000000000000000.

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

Bawasan ang fraction \frac{1000000000000000000000000000000000000000000000000}{70270417351195725177544929364088736997883993316} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 4.

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

I-multiply ang 1 at \frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329} para makuha ang \frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}.

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

Ipakita ang \frac{\frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}}{7.115369722384195} bilang isang single fraction.

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

I-multiply ang 17567604337798931294386232341022184249470998329 at 7.115369722384195 para makuha ang 124999999999999761604594726581613146873250254105.004704741010155.

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

I-expand ang \frac{250000000000000000000000000000000000000000000000}{124999999999999761604594726581613146873250254105.004704741010155} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 1000000000000000.

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

Bawasan ang fraction \frac{250000000000000000000000000000000000000000000000000000000000000}{124999999999999761604594726581613146873250254105004704741010155} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 5.

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