Solve 2tan20^circ/1+tan^230=

$$\frac { 2 \tan 20 ^ { \circ } } { 1 + \tan ^ { 2 } 30 } =$$

Evaluate

$$0.54595535139930351$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{2 \cdot 0.36397023426620234}{1 + \tan^{2}(30)}$$

Multiply 2 and 0.36397023426620234 to get 0.72794046853240468.

$$\frac{0.72794046853240468}{1+\left(\tan(30)\right)^{2}}$$

Get the value of \tan(30) from trigonometric values table.

$$\frac{0.72794046853240468}{1+\left(\frac{\sqrt{3}}{3}\right)^{2}}$$

To raise \frac{\sqrt{3}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{0.72794046853240468}{1+\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3^{2}}{3^{2}}.

$$\frac{0.72794046853240468}{\frac{3^{2}}{3^{2}}+\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}}$$

Since \frac{3^{2}}{3^{2}} and \frac{\left(\sqrt{3}\right)^{2}}{3^{2}} have the same denominator, add them by adding their numerators.

$$\frac{0.72794046853240468}{\frac{3^{2}+\left(\sqrt{3}\right)^{2}}{3^{2}}}$$

Divide 0.72794046853240468 by \frac{3^{2}+\left(\sqrt{3}\right)^{2}}{3^{2}} by multiplying 0.72794046853240468 by the reciprocal of \frac{3^{2}+\left(\sqrt{3}\right)^{2}}{3^{2}}.

$$\frac{0.72794046853240468\times 3^{2}}{3^{2}+\left(\sqrt{3}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{0.72794046853240468\times 9}{3^{2}+\left(\sqrt{3}\right)^{2}}$$

Multiply 0.72794046853240468 and 9 to get 6.55146421679164212.

$$\frac{6.55146421679164212}{3^{2}+\left(\sqrt{3}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{6.55146421679164212}{9+\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{6.55146421679164212}{9+3}$$

Add 9 and 3 to get 12.

$$\frac{6.55146421679164212}{12}$$

Expand \frac{6.55146421679164212}{12} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{655146421679164212}{1200000000000000000}$$

Reduce the fraction \frac{655146421679164212}{1200000000000000000} to lowest terms by extracting and canceling out 12.

$$\frac{54595535139930351}{100000000000000000}$$