求解 tan10^circ+1/tan10^circ

$$\tan 10 ^ { \circ } + \frac { 1 } { \tan 10 ^ { \circ } }$$

求值

$$\frac{2577728010314408453050608569716001}{440817451771162450000000000000000}\approx 5.8476088$$

求解步骤

对题中的三角函数求值

$$0.17632698070846498 + \frac{1}{0.17632698070846498}$$

将分子和分母同时乘以 100000000000000000 以展开 \frac{1}{0.17632698070846498}。

$$0.17632698070846498+\frac{100000000000000000}{17632698070846498}$$

通过求根和消去 2，将分数 \frac{100000000000000000}{17632698070846498} 降低为最简分数。

$$0.17632698070846498+\frac{50000000000000000}{8816349035423249}$$

将十进制数 0.17632698070846498 转换为分数 \frac{8816349035423249}{10000000000}。 通过求根和消去 1，将分数 \frac{8816349035423249}{10000000000} 降低为最简分数。

$$\frac{8816349035423249}{50000000000000000}+\frac{50000000000000000}{8816349035423249}$$

50000000000000000 和 8816349035423249 的最小公倍数是 440817451771162450000000000000000。将 \frac{8816349035423249}{50000000000000000} 和 \frac{50000000000000000}{8816349035423249} 转换为带分母 440817451771162450000000000000000 的分数。

$$\frac{77728010314408453050608569716001}{440817451771162450000000000000000}+\frac{2500000000000000000000000000000000}{440817451771162450000000000000000}$$

由于 \frac{77728010314408453050608569716001}{440817451771162450000000000000000} 和 \frac{2500000000000000000000000000000000}{440817451771162450000000000000000} 具有相同的分母，可通过分子相加来求和。

$$\frac{77728010314408453050608569716001+2500000000000000000000000000000000}{440817451771162450000000000000000}$$

77728010314408453050608569716001 与 2500000000000000000000000000000000 相加，得到 2577728010314408453050608569716001。

$$\frac{2577728010314408453050608569716001}{440817451771162450000000000000000}$$