Solve sqrt{3}sin60^circ+tan60^circ-2cos^230^circ

$$\sqrt { 3 } \sin 60 ^ { \circ } + \tan 60 ^ { \circ } - 2 \cos ^ { 2 } 30 ^ { \circ }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Short Solution Steps

Get the value of \sin(60) from trigonometric values table.

$$\sqrt{3}\times \frac{\sqrt{3}}{2}+\tan(60)-2\left(\cos(30)\right)^{2}$$

Express \sqrt{3}\times \frac{\sqrt{3}}{2} as a single fraction.

$$\frac{\sqrt{3}\sqrt{3}}{2}+\tan(60)-2\left(\cos(30)\right)^{2}$$

Get the value of \tan(60) from trigonometric values table.

$$\frac{\sqrt{3}\sqrt{3}}{2}+\sqrt{3}-2\left(\cos(30)\right)^{2}$$

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

$$\frac{\sqrt{3}\sqrt{3}}{2}+\frac{2\sqrt{3}}{2}-2\left(\cos(30)\right)^{2}$$

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

$$\frac{\sqrt{3}\sqrt{3}+2\sqrt{3}}{2}-2\left(\cos(30)\right)^{2}$$

Do the multiplications in \sqrt{3}\sqrt{3}+2\sqrt{3}.

$$\frac{3+2\sqrt{3}}{2}-2\left(\cos(30)\right)^{2}$$

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

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

To raise \frac{\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Express 2\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} as a single fraction.

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

Cancel out 2 in both numerator and denominator.

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

The square of \sqrt{3} is 3.

$$\frac{3+2\sqrt{3}}{2}-\frac{3}{2}$$

Since \frac{3+2\sqrt{3}}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3+2\sqrt{3}-3}{2}$$

Do the calculations in 3+2\sqrt{3}-3.

$$\frac{2\sqrt{3}}{2}$$

Cancel out 2 and 2.

$$\sqrt{3}$$