Solve (frac{sin20^{circ}tan40^circ}{tan40^circ-sin20^circ})^2

$$( \frac { \sin 20 ^ { \circ } \tan 40 ^ { \circ } } { \tan 40 ^ { \circ } - \sin 20 ^ { \circ } } ) ^ { 2 }$$

Evaluate

$$\frac{823626724142733504191598392509849145361586615684979810335489569}{2470880172428200865641504359654400000000000000000000000000000000}\approx 0.333333333$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(\frac{0.3420201433256687 \cdot 0.8390996311772799}{0.8390996311772799 - 0.3420201433256687})} ^ {2}$$

Multiply 0.3420201433256687 and 0.8390996311772799 to get 0.28698897611976901580500991456913.

$$\left(\frac{0.28698897611976901580500991456913}{0.8390996311772799-0.3420201433256687}\right)^{2}$$

Subtract 0.3420201433256687 from 0.8390996311772799 to get 0.4970794878516112.

$$\left(\frac{0.28698897611976901580500991456913}{0.4970794878516112}\right)^{2}$$

Expand \frac{0.28698897611976901580500991456913}{0.4970794878516112} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$\left(\frac{28698897611976901580500991456913}{49707948785161120000000000000000}\right)^{2}$$

Calculate \frac{28698897611976901580500991456913}{49707948785161120000000000000000} to the power of 2 and get \frac{823626724142733504191598392509849145361586615684979810335489569}{2470880172428200865641504359654400000000000000000000000000000000}.

$$\frac{823626724142733504191598392509849145361586615684979810335489569}{2470880172428200865641504359654400000000000000000000000000000000}$$