求解 frac{2sin(pi-60^{circ})cos(2pi-60^circ)tan(-60^circ+pi)}{tan(pi+60^circ)sin(-pi-60^circ)}=

$$\frac{ 2 \sin ( \pi -60 ^ { \circ } ) \cos ( 2 \pi -60 ^ { \circ } ) \tan ( -60 ^ { \circ } + \pi ) }{ \tan ( \pi +60 ^ { \circ } ) \sin ( - \pi -60 ^ { \circ } ) } =$$

求值

$$\frac{2233401796555697639851657845413273164874898249}{1172496512795457470904032307720312500000000000}\approx 1.904825961$$

求解步骤

对题中的三角函数求值

$$\frac{2 \cdot -0.30481062110221346 \cdot -0.9524129804151562 \cdot -0.3200403893795592}{0.32004038937956675 \cdot -0.30481062110221996}$$

将 2 与 -0.30481062110221346 相乘，得到 -0.60962124220442692。

$$\frac{-0.60962124220442692\left(-0.9524129804151562\right)\left(-0.3200403893795592\right)}{0.32004038937956675\left(-0.30481062110221996\right)}$$

将 -0.60962124220442692 与 -0.9524129804151562 相乘，得到 0.580611184212308050422291103284904。

$$\frac{0.580611184212308050422291103284904\left(-0.3200403893795592\right)}{0.32004038937956675\left(-0.30481062110221996\right)}$$

将 0.580611184212308050422291103284904 与 -0.3200403893795592 相乘，得到 -0.1858190294734340436356579327383843273175915343168。

$$\frac{-0.1858190294734340436356579327383843273175915343168}{0.32004038937956675\left(-0.30481062110221996\right)}$$

将 0.32004038937956675 与 -0.30481062110221996 相乘，得到 -0.09755170986458206157921548800233。

$$\frac{-0.1858190294734340436356579327383843273175915343168}{-0.09755170986458206157921548800233}$$

将分子和分母同时乘以 10000000000000000000000000000000000000000000000000 以展开 \frac{-0.1858190294734340436356579327383843273175915343168}{-0.09755170986458206157921548800233}。

$$\frac{-1858190294734340436356579327383843273175915343168}{-975517098645820615792154880023300000000000000000}$$

通过求根和消去 -832，将分数 \frac{-1858190294734340436356579327383843273175915343168}{-975517098645820615792154880023300000000000000000} 降低为最简分数。

$$\frac{2233401796555697639851657845413273164874898249}{1172496512795457470904032307720312500000000000}$$