Solve tan57^circ+cot37^circ/tan33^circ+cot53^circ

$$\frac { \tan 57 ^ { \circ } + \cot 37 ^ { \circ } } { \tan 33 ^ { \circ } + \cot 53 ^ { \circ } }$$

Evaluate

$$\frac{28669097854349927}{14029616433003049}\approx 2.043469826$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1.5398649638145827 + 1.32704482162041}{0.6494075931975106 + 0.7535540501027943}$$

Add 1.5398649638145827 and 1.32704482162041 to get 2.8669097854349927.

$$\frac{2.8669097854349927}{0.6494075931975106+0.7535540501027943}$$

Add 0.6494075931975106 and 0.7535540501027943 to get 1.4029616433003049.

$$\frac{2.8669097854349927}{1.4029616433003049}$$

Expand \frac{2.8669097854349927}{1.4029616433003049} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{28669097854349927}{14029616433003049}$$

Factor

$$\frac{13 \cdot 229 \cdot 2383 \cdot 4041207497}{103 \cdot 23041 \cdot 5911630063} = 2\frac{609864988343832}{14029616433003048} = 2.0434698262248423$$