解決2*1divtan(8^{circ})*1divtan(17^circ)*1divtan(45^circ)*1divtan(73^circ)*1divtan(82^circ) |Microsoft數學求解器

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

評估

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

解題步驟

對題中的三角函數求值

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

將 2 乘上 1 得到 2。

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

同時對分子與分母乘上 100000000000000000 以展開 \frac{2}{0.14054083470239145}。

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

透過找出與消去 5，對分式 \frac{200000000000000000}{14054083470239145} 約分至最低項。

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

將 \frac{40000000000000000}{2810816694047829} 乘上 1 得到 \frac{40000000000000000}{2810816694047829}。

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

運算式 \frac{\frac{40000000000000000}{2810816694047829}}{0.3057306814586604} 為最簡分數。

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

將 2810816694047829 乘上 0.3057306814586604 得到 859352903326621.7159602038682716。

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

同時對分子與分母乘上 10000000000000000 以展開 \frac{40000000000000000}{859352903326621.7159602038682716}。

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

透過找出與消去 4，對分式 \frac{400000000000000000000000000000000}{8593529033266217159602038682716} 約分至最低項。

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

將 \frac{100000000000000000000000000000000}{2148382258316554289900509670679} 乘上 1 得到 \frac{100000000000000000000000000000000}{2148382258316554289900509670679}。

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

從三角函數數值表格中取得 \tan(45) 的值。

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

任何項目除以一結果都為其本身。

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

將 1 乘上 \frac{100000000000000000000000000000000}{2148382258316554289900509670679} 得到 \frac{100000000000000000000000000000000}{2148382258316554289900509670679}。

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

運算式 \frac{\frac{100000000000000000000000000000000}{2148382258316554289900509670679}}{3.2708526184841404} 為最簡分數。

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

將 2148382258316554289900509670679 乘上 3.2708526184841404 得到 7027041735119572517754492936408.8736997883993316。

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

同時對分子與分母乘上 10000000000000000 以展開 \frac{100000000000000000000000000000000}{7027041735119572517754492936408.8736997883993316}。

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

透過找出與消去 4，對分式 \frac{1000000000000000000000000000000000000000000000000}{70270417351195725177544929364088736997883993316} 約分至最低項。

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

將 1 乘上 \frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329} 得到 \frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}。

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

運算式 \frac{\frac{250000000000000000000000000000000000000000000000}{17567604337798931294386232341022184249470998329}}{7.115369722384195} 為最簡分數。

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

將 17567604337798931294386232341022184249470998329 乘上 7.115369722384195 得到 124999999999999761604594726581613146873250254105.004704741010155。

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

同時對分子與分母乘上 1000000000000000 以展開 \frac{250000000000000000000000000000000000000000000000}{124999999999999761604594726581613146873250254105.004704741010155}。

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

透過找出與消去 5，對分式 \frac{250000000000000000000000000000000000000000000000000000000000000}{124999999999999761604594726581613146873250254105004704741010155} 約分至最低項。

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