求解 tan^218-tan^212/1-tan^218tan^212

$$\frac { \tan ^ { 2 } 18 - \tan ^ { 2 } 12 } { 1 - \tan ^ { 2 } 18 \tan ^ { 2 } 12 }$$

求值

$$\frac{86275024415860280357555900130400000000000000000000000000000000}{1421757413816750011084572038072202330886683359109486011143105153}\approx 0.060681959$$

求解步骤

对题中的三角函数求值

$$\frac{0.3249196962329063 ^ {2} - 0.2125565616700221 ^ {2}}{1 - 0.3249196962329063 ^ {2} 0.2125565616700221 ^ {2}}$$

计算 2 的 0.3249196962329063 乘方，得到 0.10557280900008410443921494457969。

$$\frac{0.10557280900008410443921494457969-0.2125565616700221^{2}}{1-0.3249196962329063^{2}\times 0.2125565616700221^{2}}$$

计算 2 的 0.2125565616700221 乘方，得到 0.04518029190898190818892581448841。

$$\frac{0.10557280900008410443921494457969-0.04518029190898190818892581448841}{1-0.3249196962329063^{2}\times 0.2125565616700221^{2}}$$

将 0.10557280900008410443921494457969 减去 0.04518029190898190818892581448841，得到 0.06039251709110219625028913009128。

$$\frac{0.06039251709110219625028913009128}{1-0.3249196962329063^{2}\times 0.2125565616700221^{2}}$$

计算 2 的 0.3249196962329063 乘方，得到 0.10557280900008410443921494457969。

$$\frac{0.06039251709110219625028913009128}{1-0.10557280900008410443921494457969\times 0.2125565616700221^{2}}$$

计算 2 的 0.2125565616700221 乘方，得到 0.04518029190898190818892581448841。

$$\frac{0.06039251709110219625028913009128}{1-0.10557280900008410443921494457969\times 0.04518029190898190818892581448841}$$

将 0.10557280900008410443921494457969 与 0.04518029190898190818892581448841 相乘，得到 0.0047698103282749922407995733494583683793216486233597921998263929。

$$\frac{0.06039251709110219625028913009128}{1-0.0047698103282749922407995733494583683793216486233597921998263929}$$

将 1 减去 0.0047698103282749922407995733494583683793216486233597921998263929，得到 0.9952301896717250077592004266505416316206783513766402078001736071。

$$\frac{0.06039251709110219625028913009128}{0.9952301896717250077592004266505416316206783513766402078001736071}$$

将分子和分母同时乘以 10000000000000000000000000000000000000000000000000000000000000000 以展开 \frac{0.06039251709110219625028913009128}{0.9952301896717250077592004266505416316206783513766402078001736071}。

$$\frac{603925170911021962502891300912800000000000000000000000000000000}{9952301896717250077592004266505416316206783513766402078001736071}$$

通过求根和消去 7，将分数 \frac{603925170911021962502891300912800000000000000000000000000000000}{9952301896717250077592004266505416316206783513766402078001736071} 降低为最简分数。

$$\frac{86275024415860280357555900130400000000000000000000000000000000}{1421757413816750011084572038072202330886683359109486011143105153}$$