Solve tan20^circ+tan40^circ+sqrt{3}tan20^circtan40^circ

$$\tan 20 ^ { \circ } + \tan 40 ^ { \circ } + \sqrt { 3 } \tan 20 ^ { \circ } \tan 40 ^ { \circ }$$

Evaluate

$$\frac{152703644666139272999512732107483\sqrt{3}}{500000000000000000000000000000000}+1.20306986544348224\approx 1.732050808$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.36397023426620234 + 0.8390996311772799 + \sqrt{3} 0.36397023426620234 \cdot 0.8390996311772799$$

Add 0.36397023426620234 and 0.8390996311772799 to get 1.20306986544348224.

$$1.20306986544348224+0.36397023426620234\times 0.8390996311772799\sqrt{3}$$

Multiply 0.36397023426620234 and 0.8390996311772799 to get 0.305407289332278545999025464214966.

$$1.20306986544348224+0.305407289332278545999025464214966\sqrt{3}$$