Solve 1+2cos(30^circ)-2+sqrt{3}-{left(1/2right)}^2

$$1+2 \cos ( 30 ^ { \circ } ) -2+ \sqrt{ 3 } - { \left( \frac{ 1 }{ 2 } \right) }^{ 2 }$$

Evaluate

$$2\sqrt{3}-\frac{5}{4}\approx 2.214101615$$

Solution Steps

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

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

Cancel out 2 and 2.

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

Subtract 2 from 1 to get -1.

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

Combine \sqrt{3} and \sqrt{3} to get 2\sqrt{3}.

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

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$-1+2\sqrt{3}-\frac{1}{4}$$

Subtract \frac{1}{4} from -1 to get -\frac{5}{4}.

$$-\frac{5}{4}+2\sqrt{3}$$