求解 sin(64)+cos(26)divsec(26)+cosh(64)

$$\sin ( 64 ) + \cos ( 26 ) \div \sec ( 26 ) + \cosh ( 64 )$$

求值

$$\frac{4725924400211783702918078443099}{1390752425593986000000000000000}\approx 3.398106171$$

求解步骤

对题中的三角函数求值

$$0.898794046299167 + 0.898794046299167 / 1.1126019404751888 + 1.6914813873742545$$

将分子和分母同时乘以 10000000000000000 以展开 \frac{0.898794046299167}{1.1126019404751888}。

$$0.898794046299167+\frac{8987940462991670}{11126019404751888}+1.6914813873742545$$

通过求根和消去 2，将分数 \frac{8987940462991670}{11126019404751888} 降低为最简分数。

$$0.898794046299167+\frac{4493970231495835}{5563009702375944}+1.6914813873742545$$

将十进制数 0.898794046299167 转换为分数 \frac{898794046299167}{10000000000}。 通过求根和消去 1，将分数 \frac{898794046299167}{10000000000} 降低为最简分数。

$$\frac{898794046299167}{1000000000000000}+\frac{4493970231495835}{5563009702375944}+1.6914813873742545$$

1000000000000000 和 5563009702375944 的最小公倍数是 695376212796993000000000000000。将 \frac{898794046299167}{1000000000000000} 和 \frac{4493970231495835}{5563009702375944} 转换为带分母 695376212796993000000000000000 的分数。

$$\frac{624999999999999930557516004831}{695376212796993000000000000000}+\frac{561746278936979375000000000000}{695376212796993000000000000000}+1.6914813873742545$$

由于 \frac{624999999999999930557516004831}{695376212796993000000000000000} 和 \frac{561746278936979375000000000000}{695376212796993000000000000000} 具有相同的分母，可通过分子相加来求和。

$$\frac{624999999999999930557516004831+561746278936979375000000000000}{695376212796993000000000000000}+1.6914813873742545$$

624999999999999930557516004831 与 561746278936979375000000000000 相加，得到 1186746278936979305557516004831。

$$\frac{1186746278936979305557516004831}{695376212796993000000000000000}+1.6914813873742545$$

将十进制数 1.6914813873742545 转换为分数 \frac{3382962774748509}{10000000000}。 通过求根和消去 1，将分数 \frac{3382962774748509}{10000000000} 降低为最简分数。

$$\frac{1186746278936979305557516004831}{695376212796993000000000000000}+\frac{3382962774748509}{2000000000000000}$$

695376212796993000000000000000 和 2000000000000000 的最小公倍数是 1390752425593986000000000000000。将 \frac{1186746278936979305557516004831}{695376212796993000000000000000} 和 \frac{3382962774748509}{2000000000000000} 转换为带分母 1390752425593986000000000000000 的分数。

$$\frac{2373492557873958611115032009662}{1390752425593986000000000000000}+\frac{2352431842337825091803046433437}{1390752425593986000000000000000}$$

由于 \frac{2373492557873958611115032009662}{1390752425593986000000000000000} 和 \frac{2352431842337825091803046433437}{1390752425593986000000000000000} 具有相同的分母，可通过分子相加来求和。

$$\frac{2373492557873958611115032009662+2352431842337825091803046433437}{1390752425593986000000000000000}$$

2373492557873958611115032009662 与 2352431842337825091803046433437 相加，得到 4725924400211783702918078443099。

$$\frac{4725924400211783702918078443099}{1390752425593986000000000000000}$$

因式分解

$$\frac{4725924400211783702918078443099}{3 \cdot 7 \cdot 13 \cdot 19 \cdot 41 \cdot 3269788979 \cdot 2 ^ {16} \cdot 5 ^ {15}} = 3\frac{5.536671234298255 \times 10^{29}}{1.390752425593986 \times 10^{30}} = 3.3981061713362504$$