求解 {l}{sin2}{+1/cos2}

$$\left. \begin{array} { l } { \sin 2 } \\ { + \frac { 1 } { \cos 2 } } \end{array} \right.$$

求值

$$\frac{517439118436031325592866904011463}{499695413509547900000000000000000}\approx 1.035509041$$

求解步骤

对题中的三角函数求值

$$0.03489949670250097 + \frac{1}{0.9993908270190958}$$

将分子和分母同时乘以 10000000000000000 以展开 \frac{1}{0.9993908270190958}。

$$0.03489949670250097+\frac{10000000000000000}{9993908270190958}$$

通过求根和消去 2，将分数 \frac{10000000000000000}{9993908270190958} 降低为最简分数。

$$0.03489949670250097+\frac{5000000000000000}{4996954135095479}$$

将十进制数 0.03489949670250097 转换为分数 \frac{3489949670250097}{10000000000}。 通过求根和消去 1，将分数 \frac{3489949670250097}{10000000000} 降低为最简分数。

$$\frac{3489949670250097}{100000000000000000}+\frac{5000000000000000}{4996954135095479}$$

100000000000000000 和 4996954135095479 的最小公倍数是 499695413509547900000000000000000。将 \frac{3489949670250097}{100000000000000000} 和 \frac{5000000000000000}{4996954135095479} 转换为带分母 499695413509547900000000000000000 的分数。

$$\frac{17439118436031325592866904011463}{499695413509547900000000000000000}+\frac{500000000000000000000000000000000}{499695413509547900000000000000000}$$

由于 \frac{17439118436031325592866904011463}{499695413509547900000000000000000} 和 \frac{500000000000000000000000000000000}{499695413509547900000000000000000} 具有相同的分母，可通过分子相加来求和。

$$\frac{17439118436031325592866904011463+500000000000000000000000000000000}{499695413509547900000000000000000}$$

17439118436031325592866904011463 与 500000000000000000000000000000000 相加，得到 517439118436031325592866904011463。

$$\frac{517439118436031325592866904011463}{499695413509547900000000000000000}$$