求解 cos6/tan12=csc12/tan99

$$\frac { \cos 6 } { \tan 12 } = \frac { \csc 12 } { \tan 99 }$$

验证

求解步骤

对题中的三角函数求值

$$\frac{0.9945218953682733}{0.2125565616700221} = \frac{4.809734344744132}{-6.313751514675037}$$

将分子和分母同时乘以 10000000000000000 以展开 \frac{0.9945218953682733}{0.2125565616700221}。

$$\frac{9945218953682733}{2125565616700221}=\frac{4.809734344744132}{-6.313751514675037}$$

通过求根和消去 3，将分数 \frac{9945218953682733}{2125565616700221} 降低为最简分数。

$$\frac{3315072984560911}{708521872233407}=\frac{4.809734344744132}{-6.313751514675037}$$

将分子和分母同时乘以 1000000000000000 以展开 \frac{4.809734344744132}{-6.313751514675037}。

$$\frac{3315072984560911}{708521872233407}=\frac{4809734344744132}{-6313751514675037}$$

可通过提取负号，将分数 \frac{4809734344744132}{-6313751514675037} 重写为 -\frac{4809734344744132}{6313751514675037}。

$$\frac{3315072984560911}{708521872233407}=-\frac{4809734344744132}{6313751514675037}$$

708521872233407 和 6313751514675037 的最小公倍数是 4473431043994066486695020361059。将 \frac{3315072984560911}{708521872233407} 和 -\frac{4809734344744132}{6313751514675037} 转换为带分母 4473431043994066486695020361059 的分数。

$$\frac{20930547077529747373748297678707}{4473431043994066486695020361059}=-\frac{3407801982883431429858797617724}{4473431043994066486695020361059}$$

比较 \frac{20930547077529747373748297678707}{4473431043994066486695020361059} 和 -\frac{3407801982883431429858797617724}{4473431043994066486695020361059}。

$$\text{false}$$