Solve 2sin30^circ-2/sqrt{3}cos30^circ

$$2 \sin 30 ^ { \circ } - \frac { 2 } { \sqrt { 3 } } \cos 30 ^ { \circ }$$

Evaluate

$$0$$

Solution Steps

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

$$2\times \frac{1}{2}-\frac{2}{\sqrt{3}}\cos(30)$$

Multiply 2 and \frac{1}{2} to get 1.

$$1-\frac{2}{\sqrt{3}}\cos(30)$$

Rationalize the denominator of \frac{2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$1-\frac{2\sqrt{3}}{3}\cos(30)$$

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

$$1-\frac{2\sqrt{3}}{3}\times \frac{\sqrt{3}}{2}$$

Multiply \frac{2\sqrt{3}}{3} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{2\sqrt{3}\sqrt{3}}{3\times 2}$$

Cancel out 2 in both numerator and denominator.

$$1-\frac{\sqrt{3}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$1-\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$1-1$$

Subtract 1 from 1 to get 0.

$$0$$